Question

Find the zeroes of the quadratic polynomial $x^2-3x-28$ and verify the relationship between the zeros and the coefficients.

Answer 1

Let us find the coefficients.
a = 1,
b = -3
c = -28

Step 1:
Find the zeroes
Hence, the zeroes are -4 and 7.


Step 2:

Verification -

From step 1,we know that the zeroes are -4 and 7.

Sum of roots = - 4 + 7 = 3
Product of Zeros = $-4\times 7$ = - 28

Now looking at the polynomial, we know that
Sum of zeroes = $\frac{-b}{a}$
= - $\frac{-3}{1}$
= 3
Product of zeroes = $\frac{c}{a}$

=$\frac{-28}{1}$

= - 28
Hence, verified.