Question

find the quadratic polynomial whose zeros are-3 and 4

Answer 1

the answer is x^2 + 7x + 12

Answer 2

$\huge\bold\red{Question}$

Find the quadratic polynomial whose zeros are-3 and 4

$\huge\bold\green{Solution}$

Let us assume quadratic polynomial be $\bold{ax²+bx+c=0}$, where $\bold{a≠0}$ and it’s zeroes be $\bold{α}$ and $\bold{β}$.

Here

$\bold{α = -3}$

$\bold{β = 4}$

We know that

(1) Sum of the zeroes

$\bold{⇒\:α+ β=}$ $\bold{\frac{ - b}{a}}$

$\bold{⇒\: -3 + 4 =}$ $\bold{\frac{ - b}{a}}$

$\bold{⇒\:1}$ = $\bold{\frac{ - b}{a}}$

$\bold{\frac{ - b}{a}}$ $\bold{=-1…………………eqn\:(i)}$

(2) Product of the zeroes

$\bold{⇒ α × β = \frac{c}{a}}$

$\bold{⇒-3 × 4 = \frac{c}{a}}$

$\bold{\frac{c}{a} = -12…………………eqn(ii)}$

∴ The quadratic polynomial is $\bold{ax^2+bx+c}$ is

Where $\bold{,a = 1, b= -1}$ and $\bold{c= -12}$

Substitute the values in the above equation we get

$\bold{x^2 – x – 12 = 0}$