For the quadratic equation $4 x^{2} - 8 x + 3 = 0$ , find the sum and the product of its roots.

medium 2 marks Class 9 · Mathematics · Polynomials

Answer

Sum = 2, Product = \tfrac{3}{4}

The correct answer is Sum = 2, Product = \tfrac{3}{4} — The product of the roots is $\frac{c}{a} = \frac{3}{4}$ .

Step-by-step solution

Write the equation in standard form $a x^{2} + b x + c = 0$ ; here $a = 4$ , $b = - 8$ , $c = 3$ .
The sum of the roots is $- \frac{b}{a} = - \frac{- 8}{4} = \frac{8}{4} = 2$ .
The product of the roots is $\frac{c}{a} = \frac{3}{4}$ .

Common mistake: Using the wrong sign for the sum of roots

Concept tested: Vieta's formulas for quadratics