Question 53

If sum of the roots of a quadratic equation is 7 and product of the roots is 12. Find the quadratic equation.

Solution

A quadratic equation is of the form : $$x^2 - $$(sum of roots) $$x + $$(product of roots) $$= 0$$

Let the roots of equation are $$\alpha$$ and $$\beta$$

=> Sum of roots = $$\alpha + \beta = 7$$

Product of roots = $$\alpha \beta = 12$$

Equation : $$x^2 - (\alpha + \beta) x + \alpha \beta = 0$$

=> $$x^2 - 7x + 12 = 0$$

=> Ans - (A)

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If sum of the roots of a quadratic equation is ­7 and product of the roots is 12. Find the quadratic equation.