Question

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients.

$63-2x-x^2$

• A. $7,3$
• B. $7,7$
• C. $7,-9$
• D. $7,-2$

Answer 1

Answer: (C)

$7,-9$

$63-2x-x^2$

$=-x^2-2x+63$

$=-x^2-9x+7x+63$

$=-x(x+9)+7(x+9)$

$=(x+9)(-x+7)$

$x=-9$ , $x=7$

The zeros of the polynomials are $-9$,$7$

Relationship between the zeros and the coefficients of the polynomials-

Sum of the zeros=-$\frac{coefficientofx}{coefficientof{x}^2}=-\left(\frac{-2}{-1}\right)=-2$

Also sum of zeros=$-9+7$ =$-2$

Product of the zeros =$\frac{constantterm}{coefficientof{x}^2}=\frac{63}{-1}=-63$

Also the product of the zeros= $-9\times 7=-63$

Hence verified.