Let α and β are the zeroes of the polynomial ax² + bx + c, then we have α + β = √2 = (3√2)/3 = (-b)/a αβ = 1/3 = c/a On comparing, a = 3, b =-3/√2 and c = 1 Hence, the required quadratic polynomial is 3x² - 3/√2 + 1. Video Explanation 😃 Understanding polynomials is essential for further study in matRead more
Let α and β are the zeroes of the polynomial ax² + bx + c, then we have
α + β = √2 = (3√2)/3 = (-b)/a
αβ = 1/3 = c/a
On comparing,
a = 3, b =-3/√2 and c = 1
Hence, the required quadratic polynomial is 3x² – 3/√2 + 1.
Video Explanation 😃
Understanding polynomials is essential for further study in mathematics, including topics such as algebra and calculus. Studying polynomials helps students develop important mathematical skills, such as algebraic manipulation, problem-solving, and critical thinking.
Let α and β are the zeroes of the polynomial ax² + bx + c, then we have α + β = 1 = 1/1 = (-b)/a αβ = 1 = 1/1 c/a On comparing, a = 1, b = -1 and c = 1 Hence, the required quadratic polynomial is x² - x + 1. Explanation 👇
Let α and β are the zeroes of the polynomial ax² + bx + c, then we have
α + β = 1 = 1/1 = (-b)/a
αβ = 1 = 1/1 c/a
On comparing,
a = 1, b = -1 and c = 1
Hence, the required quadratic polynomial is x² – x + 1.
Let α and β are the zeroes of the polynomial ax² + bx + c, then we have α + β = 1/4 = (-b)/a αβ = -1 = (-4)/4 = c/a On comparing, a = 4, b = -1 and c = -4 Hence, the required quadratic polynomial is 4x² - x - 4. See here 👇
Let α and β are the zeroes of the polynomial ax² + bx + c, then we have
α + β = 1/4 = (-b)/a
αβ = -1 = (-4)/4 = c/a
On comparing,
a = 4, b = -1 and c = -4
Hence, the required quadratic polynomial is 4x² – x – 4.
3x² - x - 4 = 3x² - 4x + 3x - 4 = x(3x - 4) + 1(3x - 4) = (3x - 4)(x + 1) The value of 3x² - x - 4 is zero if 3x - 4 0 or x + 1 0. ⇒ x = 4/3 or x = -1. Therefore, the zeroes of 3x² - x - 4 are and -1. Now, Sum of zeroes = 4/3 +(-1) = (4 - 3)/3 = 1/3 = -(-1)/3 = -(Coficient of x)/(Cofficient of x²) PRead more
3x² – x – 4
= 3x² – 4x + 3x – 4
= x(3x – 4) + 1(3x – 4)
= (3x – 4)(x + 1)
The value of 3x² – x – 4 is zero if 3x – 4 0 or x + 1 0.
⇒ x = 4/3 or x = -1.
Therefore, the zeroes of 3x² – x – 4 are and -1.
Now, Sum of zeroes = 4/3 +(-1) = (4 – 3)/3 = 1/3 = -(-1)/3 = -(Coficient of x)/(Cofficient of x²)
Product of zeroes = 4/3 × (-1) = -4/3 = (-4)/3 = (Coefficient of term)/(Cofficient of x²)
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: p(x) = x ³ – 3x² + 5x – 3, g(x) = x² – 2
Here is the Video Solution 😃
Here is the Video Solution 😃
See lessFind a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. √(2 ) ,1/3
Let α and β are the zeroes of the polynomial ax² + bx + c, then we have α + β = √2 = (3√2)/3 = (-b)/a αβ = 1/3 = c/a On comparing, a = 3, b =-3/√2 and c = 1 Hence, the required quadratic polynomial is 3x² - 3/√2 + 1. Video Explanation 😃 Understanding polynomials is essential for further study in matRead more
Let α and β are the zeroes of the polynomial ax² + bx + c, then we have
α + β = √2 = (3√2)/3 = (-b)/a
αβ = 1/3 = c/a
On comparing,
a = 3, b =-3/√2 and c = 1
Hence, the required quadratic polynomial is 3x² – 3/√2 + 1.
Video Explanation 😃
See lessUnderstanding polynomials is essential for further study in mathematics, including topics such as algebra and calculus. Studying polynomials helps students develop important mathematical skills, such as algebraic manipulation, problem-solving, and critical thinking.
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. 1,1
Let α and β are the zeroes of the polynomial ax² + bx + c, then we have α + β = 1 = 1/1 = (-b)/a αβ = 1 = 1/1 c/a On comparing, a = 1, b = -1 and c = 1 Hence, the required quadratic polynomial is x² - x + 1. Explanation 👇
Let α and β are the zeroes of the polynomial ax² + bx + c, then we have
α + β = 1 = 1/1 = (-b)/a
αβ = 1 = 1/1 c/a
On comparing,
a = 1, b = -1 and c = 1
Hence, the required quadratic polynomial is x² – x + 1.
Explanation 👇
See lessFind a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.1/4, -1
Let α and β are the zeroes of the polynomial ax² + bx + c, then we have α + β = 1/4 = (-b)/a αβ = -1 = (-4)/4 = c/a On comparing, a = 4, b = -1 and c = -4 Hence, the required quadratic polynomial is 4x² - x - 4. See here 👇
Let α and β are the zeroes of the polynomial ax² + bx + c, then we have
α + β = 1/4 = (-b)/a
αβ = -1 = (-4)/4 = c/a
On comparing,
a = 4, b = -1 and c = -4
Hence, the required quadratic polynomial is 4x² – x – 4.
See here 👇
See lessFind the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. 3x² – x – 4.
3x² - x - 4 = 3x² - 4x + 3x - 4 = x(3x - 4) + 1(3x - 4) = (3x - 4)(x + 1) The value of 3x² - x - 4 is zero if 3x - 4 0 or x + 1 0. ⇒ x = 4/3 or x = -1. Therefore, the zeroes of 3x² - x - 4 are and -1. Now, Sum of zeroes = 4/3 +(-1) = (4 - 3)/3 = 1/3 = -(-1)/3 = -(Coficient of x)/(Cofficient of x²) PRead more
3x² – x – 4
= 3x² – 4x + 3x – 4
= x(3x – 4) + 1(3x – 4)
= (3x – 4)(x + 1)
The value of 3x² – x – 4 is zero if 3x – 4 0 or x + 1 0.
⇒ x = 4/3 or x = -1.
Therefore, the zeroes of 3x² – x – 4 are and -1.
Now, Sum of zeroes = 4/3 +(-1) = (4 – 3)/3 = 1/3 = -(-1)/3 = -(Coficient of x)/(Cofficient of x²)
Product of zeroes = 4/3 × (-1) = -4/3 = (-4)/3 = (Coefficient of term)/(Cofficient of x²)
See Here 😃
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