Question

Find the values of p and q so that 1 and -2 are the zeroes of the polynomial
〖f(x)=x〗^3+10x^2+px+q and then find the third zero.

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

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Concept used here:-

Mathematical calculation

Given,.

f(x)=x³+10x²+px+q

And we have given 1 and -2 are zeros of the polynomial.

Replacing them in equation.

f(1)=(1)³+10(1)²+p(1)+q

f(1)=1+10+p+q

f(1)=p+q+11------>eq.1

And,.

f(-2)=(-2)³+10(-2)²+p(-2)+q

f(-2)=-8+40-2p+q

f(-2)=q-2p+32------>eq.2

Solving equations 1&2

3p=21

p=7

p+q=-11

7+q=-11

q=-18

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