Question

If the sum of the zeroes of the polynomial ax²–8x–4 is 4, then find the value of a​

Answer 1

Given,

Sum of zeroes of the quadratic polynomial ax²–8x–4 is 4.

To Find,

The value of a.

Solution,

Since we are given the sum of the roots of the equation.

Also, we know that

Sum of zeroes = -b/a

where b is the coefficient of x and a is the coefficient of x².

Sum of zeroes = -(-8)/a = 4

8/a = 4

a = 8/4

a = 2.

Hence, the value of a is 2.

Answer 2

The value of $a$ is $2$.

Concept:

If $P(x)=ax^{2}+bx+c$ be a quadratic polynomial and $\alpha,\beta$ be its zeroes, then

$\alpha+\beta=-\dfrac{b}{a}$

$\alpha\beta=\dfrac{c}{a}$

Step-by-step explanation:

The given polynomial is

$P(x)=ax^{2}-8x-4$

Given that, the sum of the zeroes of this polynomial is $4$. Then

$-\dfrac{-8}{a}=4$

$\Rightarrow \dfrac{8}{a}=4$

$\Rightarrow a=\dfrac{8}{4}$

$\Rightarrow a=2$

Thus the value of $a$ is $2$.

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