Question

9. Find the values of p and q so that the polynomial
x^3+ px^2- 37x +q is exactly divisible by x^2 -3x+2​

Answer 1

Answer:

p=10;q=26

Step-by-step explanation:

by the polynomial x^2-3x+2,

we can get x1+x2=-(-3)/1=3;

x1.x2 =2/1=2;

by solving above eqns, we get x1=2,x2=1

if the polynomial x^3+px^2-37x+q is exactly divisible by (x^2-3x+2),then the roots of (x^2-3x+2) will be the roots of above polynomial also.

therefore by substituting X1=2 in given polynomial,

2^3+(p*2^2)-(37*2)+q=0;

8+4p-74+q=0;

4p+q=66;

by substituting x2=1 in given polynomial,

1^3+(p*1^2)-(37*1)+q=0;

1+p-37+q=0;

p+q=36;

by solving those two eqns,p=10;q=26