AP EAMCET202316 May 2023Evening ShiftMathematicsQuadratic EquationActual

If x^2+x-6 is a factor of 2 x^3+x^2+a x+b , then 6 a+13 b=

Options

A305
B133
C0
D-1

Correct answer

C. 0

Step-by-step solution

Since, x^2+x-6=0 (x+3)(x-2)=0 x=-3,2 So, 2(-3)^3+(-3)^2+a(-3)+b=0 -3 a + b =45 ... (i) and 2(2)^3+(2)^2+2 a+b=0 2 a + b =-20 ... (ii) After solving (i) & (ii) we get a=-13, b=6 Now, 6 a+13 b=-65+65=0

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