Question

find the zeroes of the quadratic polynomial x2-x-30 and verify the relation between the zeroes and its coefficients​

Answer 1

The zeros of the quadratic polynomial is -5 and 6.

Step-by-step explanation:

Consider the provided polynomial.

$x^2-x-30$

Let $p(x)=x^2-x-30$

Substitute p(x)=0 and split the middle term.

$x^2-6x+5x-30=0$

$x(x-6)+5(x-6)=0$

$(x+5)(x-6)=0$

$x+5=0\ or\ x-6=0\\x=-5\ or\ x=6$

Thus, the zeros of the quadratic polynomial is -5 and 6.

Verify:

$\text{Sum of zeros}=-\frac{\text{Coefficient of }x}{\text{Coefficient of }x^2}$

$-5+6=-\frac{-1}{1}\\1=1$

Which is true.

$\text{Product of zeros}=\frac{\text{Constant term}}{\text{Coefficient of }x^2}$

$-5\times6=\frac{-30}{1}\\-30=-30$

Which is true.

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