Question

The quadratic polynomial p(x) with –24 and 4 as a product and one of the zeros respectively is

Answer 1

Given: Product of roots= -24 and 4 is one of the roots

To find: Quadratic polynomial p(x)

Solution:

Product of roots=-24

One root=4

Therefore the other root must be -24/4=-6

Sum of roots=4+(-6)=-2

Product of roots=-24

Now, we know that quadratic polynomial p(x) is given by =x^2- (sum of roots)x + Product of roots

Therefore,the equation is given by x^2+2x-24

Answer 2

Given : The quadratic polynomial p(x) with –24 and 4 as a product and one of the zeros respectively

To Find : Polynomial

Solution:

Product of zeroes =  -24

One zero = 4

Hence other zero = -24/4  = - 6

p(x) = ( x - a)(x - b)

where a nd b are zeroes

p(x) = (x -4)(x - (-6))

= ( x - 4)(x + 6)

= x² + 2x  - 24

p(x) = x² + 2x  - 24

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