Question

Find the quadratic equation whose sum of roots is 5 and whose product of roots is 6.

• A. $x^2+5x+6$
• B. $x^2-5x+6$
• C. $x^2+6x+5$
• D. $x^2-6x+5$

Answer 1

The correct option is B $x^2-5x+6$

Let the quadratic equation be $a{x}^2+bx+c$ = 0 and its roots be $\alpha$ and $\beta$.
Now, the sum of roots $\alpha$ + $\beta$ is 5 and the product of roots $\alpha \times \beta$ is 6.

From the quadratic equation we know that the sum of its roots is $\frac{-b}{a}$ and the product of roots is $\frac{c}{a}$.
The value of $\frac{-b}{a}$ = 5 and $\frac{c}{a}$ = 6
On dividing the quadratic equation $a{x}^2+bx+c$ = 0 on both sides by 'a' we get,

$x^2+\frac{b}{a}x+\frac{c}{a}$ = 0

Substituting the value of $\frac{b}{a}$ = -5 and $\frac{c}{a}$ = 6,
The equation becomes $x^2-5x+6$ = 0.