Question

Find the zeros of the following quadratic polynomials and varify the relationship between the zeros and it's Coefficient :x
$x {2} - 2x - 8$
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Answer 1

SOLUTION :-

 p(x) = x² - 2x - 8

 $\longrightarrow \sf x^2-2x-8 = 0 \\\\\longrightarrow x^2 -4x+2x-8 = 0 \\\\\longrightarrow x(x-4)+ 2(x-4) = 0 \\\\\longrightarrow (x-4)(x+2) = 0$

 Zeros of the quadratic polynomial = 4 , -2

The polynomial is in the form of ax²+ bx + c

 Where a = 1, b = -2 and c = -8

 

We know that the zeros of the polynomial are 4 and -2

 that is α = 4 and β = 2

By the relationship we know that α + β = -b/a

That is,

 4 +-2  = -(-2) / 1

 2 =2

And,

α × β = c/a

4 × -2 = -8 / 1

-8 = -8

Hence verified