2x2 – 7x + 3 = 0 Dividing both side by 2 x² - 7/2 x + 3/2 = 0 ⇒ x² - 7/2 x = - 3/2 Adding [1/2(7/2)]² on both the sides, we get x² - 7/2 x + (7/4)² = - 3/2 + (7/4)² [(as x = -b±√(b²- 4ac)]/2a] ⇒ (x - 7/4)² = - 3/2 + 49/16 ⇒ (x - 7/4)² = - 24 + 49/16 ⇒ (x - 7/4)² = 25/16 ⇒ x - 7/4 = ± 5/4 Either x -Read more
2×2 – 7x + 3 = 0
Dividing both side by 2
x² – 7/2 x + 3/2 = 0 ⇒ x² – 7/2 x = – 3/2
Adding [1/2(7/2)]² on both the sides, we get
x² – 7/2 x + (7/4)² = – 3/2 + (7/4)² [(as x = -b±√(b²- 4ac)]/2a]
⇒ (x – 7/4)² = – 3/2 + 49/16 ⇒ (x – 7/4)² = – 24 + 49/16
⇒ (x – 7/4)² = 25/16
⇒ x – 7/4 = ± 5/4
Either x – 7/4 = 5/4 or x – 7/4 = – 5/4
⇒ x = 5/4 + 7/4 or x – 5/4 + 7/4
⇒ x = 5+7/4 = 12/4 = 3 x 5+7/4 = 2/4 = 1/2
Hence, the roots of the quadratic equation are 3 and 1/2.
x2 – 2x = (–2) (3 – x) simplifying the given equation, we get x2 – 2x = (–2) (3 – x) ⇒ x² - 2x = - 6 + 2x ⇒ x² - 4x + 6 = 0 or x² - 4x + 6 = 0 This is an equation of type ax² + bx + c = 0. Hence, the given equation is a quadratic equation.
x2 – 2x = (–2) (3 – x)
simplifying the given equation, we get
x2 – 2x = (–2) (3 – x)
⇒ x² – 2x = – 6 + 2x
⇒ x² – 4x + 6 = 0
or x² – 4x + 6 = 0
This is an equation of type ax² + bx + c = 0.
Hence, the given equation is a quadratic equation.
(x – 2)(x + 1) = (x – 1)(x + 3) Simplifying the given equation, we get (x – 2)(x + 1) = (x – 1)(x + 3) ⇒ x² - 2x + x - 2 = x² - x +3x - 3 ⇒ - 3x + 1 = 0 or 3x - 1 = 0 This is not an equation of type ax² + bx + c = 0. Hence, the given equation is a quadratic equation.
(x – 2)(x + 1) = (x – 1)(x + 3)
Simplifying the given equation, we get
(x – 2)(x + 1) = (x – 1)(x + 3)
⇒ x² – 2x + x – 2 = x² – x +3x – 3
⇒ – 3x + 1 = 0
or 3x – 1 = 0
This is not an equation of type ax² + bx + c = 0.
Hence, the given equation is a quadratic equation.
x² + 3x + 1 = (x – 2)² simplifying the given equation, we get x² + 3x + 1 = (x – 2)² ⇒ x² + 3x + 1 = x² - 4x + 4 ⇒ 7x - 3 = 0 or 7x - 3 = 0 This is not an equation of type ax² + bx + c = 0. Hence, the given equation is a quadratic equation.
x² + 3x + 1 = (x – 2)²
simplifying the given equation, we get
x² + 3x + 1 = (x – 2)²
⇒ x² + 3x + 1 = x² – 4x + 4
⇒ 7x – 3 = 0
or 7x – 3 = 0
This is not an equation of type ax² + bx + c = 0.
Hence, the given equation is a quadratic equation.
(2x – 1)(x – 3) = (x + 5)(x – 1) Simplifying the given equation, we get (2x – 1)(x – 3) = (x + 5)(x – 1) ⇒ 2x² - x - 6x + 3 = x² + 5x - x - 5 ⇒ x² - 11x + 8 = 0 or x² - 11x + 8 = 0 This is an equation of type ax² + bx + c = 0. Hence, the given equation is a quadratic equation.
(2x – 1)(x – 3) = (x + 5)(x – 1)
Simplifying the given equation, we get
(2x – 1)(x – 3) = (x + 5)(x – 1)
⇒ 2x² – x – 6x + 3 = x² + 5x – x – 5
⇒ x² – 11x + 8 = 0
or x² – 11x + 8 = 0
This is an equation of type ax² + bx + c = 0.
Hence, the given equation is a quadratic equation.
Find the roots of the following quadratic equations, if they exist, by the method of completing the square: 2 x² – 7x + 3 = 0
2x2 – 7x + 3 = 0 Dividing both side by 2 x² - 7/2 x + 3/2 = 0 ⇒ x² - 7/2 x = - 3/2 Adding [1/2(7/2)]² on both the sides, we get x² - 7/2 x + (7/4)² = - 3/2 + (7/4)² [(as x = -b±√(b²- 4ac)]/2a] ⇒ (x - 7/4)² = - 3/2 + 49/16 ⇒ (x - 7/4)² = - 24 + 49/16 ⇒ (x - 7/4)² = 25/16 ⇒ x - 7/4 = ± 5/4 Either x -Read more
2×2 – 7x + 3 = 0
See lessDividing both side by 2
x² – 7/2 x + 3/2 = 0 ⇒ x² – 7/2 x = – 3/2
Adding [1/2(7/2)]² on both the sides, we get
x² – 7/2 x + (7/4)² = – 3/2 + (7/4)² [(as x = -b±√(b²- 4ac)]/2a]
⇒ (x – 7/4)² = – 3/2 + 49/16 ⇒ (x – 7/4)² = – 24 + 49/16
⇒ (x – 7/4)² = 25/16
⇒ x – 7/4 = ± 5/4
Either x – 7/4 = 5/4 or x – 7/4 = – 5/4
⇒ x = 5/4 + 7/4 or x – 5/4 + 7/4
⇒ x = 5+7/4 = 12/4 = 3 x 5+7/4 = 2/4 = 1/2
Hence, the roots of the quadratic equation are 3 and 1/2.
Check whether the following is quadratic equations : x² – 2x = (–2) (3 – x)
x2 – 2x = (–2) (3 – x) simplifying the given equation, we get x2 – 2x = (–2) (3 – x) ⇒ x² - 2x = - 6 + 2x ⇒ x² - 4x + 6 = 0 or x² - 4x + 6 = 0 This is an equation of type ax² + bx + c = 0. Hence, the given equation is a quadratic equation.
x2 – 2x = (–2) (3 – x)
See lesssimplifying the given equation, we get
x2 – 2x = (–2) (3 – x)
⇒ x² – 2x = – 6 + 2x
⇒ x² – 4x + 6 = 0
or x² – 4x + 6 = 0
This is an equation of type ax² + bx + c = 0.
Hence, the given equation is a quadratic equation.
Check whether the following is quadratic equation: (x – 2)(x + 1) = (x – 1)(x + 3)
(x – 2)(x + 1) = (x – 1)(x + 3) Simplifying the given equation, we get (x – 2)(x + 1) = (x – 1)(x + 3) ⇒ x² - 2x + x - 2 = x² - x +3x - 3 ⇒ - 3x + 1 = 0 or 3x - 1 = 0 This is not an equation of type ax² + bx + c = 0. Hence, the given equation is a quadratic equation.
(x – 2)(x + 1) = (x – 1)(x + 3)
Simplifying the given equation, we get
(x – 2)(x + 1) = (x – 1)(x + 3)
⇒ x² – 2x + x – 2 = x² – x +3x – 3
⇒ – 3x + 1 = 0
or 3x – 1 = 0
This is not an equation of type ax² + bx + c = 0.
Hence, the given equation is a quadratic equation.
See lessCheck whether the following is quadratic equation: x² + 3x + 1 = (x – 2)²
x² + 3x + 1 = (x – 2)² simplifying the given equation, we get x² + 3x + 1 = (x – 2)² ⇒ x² + 3x + 1 = x² - 4x + 4 ⇒ 7x - 3 = 0 or 7x - 3 = 0 This is not an equation of type ax² + bx + c = 0. Hence, the given equation is a quadratic equation.
x² + 3x + 1 = (x – 2)²
See lesssimplifying the given equation, we get
x² + 3x + 1 = (x – 2)²
⇒ x² + 3x + 1 = x² – 4x + 4
⇒ 7x – 3 = 0
or 7x – 3 = 0
This is not an equation of type ax² + bx + c = 0.
Hence, the given equation is a quadratic equation.
Check whether the following is quadratic equation: (2x – 1)(x – 3) = (x + 5)(x – 1)
(2x – 1)(x – 3) = (x + 5)(x – 1) Simplifying the given equation, we get (2x – 1)(x – 3) = (x + 5)(x – 1) ⇒ 2x² - x - 6x + 3 = x² + 5x - x - 5 ⇒ x² - 11x + 8 = 0 or x² - 11x + 8 = 0 This is an equation of type ax² + bx + c = 0. Hence, the given equation is a quadratic equation.
(2x – 1)(x – 3) = (x + 5)(x – 1)
See lessSimplifying the given equation, we get
(2x – 1)(x – 3) = (x + 5)(x – 1)
⇒ 2x² – x – 6x + 3 = x² + 5x – x – 5
⇒ x² – 11x + 8 = 0
or x² – 11x + 8 = 0
This is an equation of type ax² + bx + c = 0.
Hence, the given equation is a quadratic equation.