Quadratic Equation are the values of the variable and quadratic equations can be written in the form. What is the simple way to solve these quadratics. NCERT Solutions for Class 10th Maths are helpful for revision.
Chapter 4 EXERCISE 4.3 Questions No:1 Part (iv) Page No:87.
Find the roots of the following quadratic equations, if they exist, by the method of completing the square: 2x² + x + 4 = 0
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2x² + x + 4 = 0
dividing both sides by 2
x² + 1/2 x = – 2
Adding [1/2(1/2)]² on both the sides, we get
x² + 1/2 x + (1/4)² = – 2 + (1/4)² [ As x = (-b±√b²- 4ac)/2a]
⇒ (x+1/4)² = – 2 + 1/16 ⇒ (x + 1/4)² = (-32 + 1)/16
⇒ (x + 1/4)² = – 31/16 < 0
we know that the square of any real number can not be negative or (x + 1/4)² can not be negative. Hence, this quadratic equation has no real roots.