Question

What should be the value of a and b , if the value of 2x³+5x²+10x-a+3b=20 and 5x³+3x²+2x-2a+b=15 when x=-2
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Answer 1

EXPLANATION.

→ 2x³ + 5x² + 10x - a + 3b = 20. .........(1).

→ 5x³ + 3x² + 2x - 2a + b = 15 ...........(2).

When x = -2.

Case = 1.

put x = -2 in equation (1) we get,

→ 2(-2)³ + 5(-2)² + 10(-2) - a + 3b = 20.

→ - 16 + 20 - 20 - a + 3b = 20.

→ - 16 - a + 3b = 20.

→ 3b - 36 = a ...........(3).

Case = 2.

put x = -2 in equation (2) we get,

→ 5(-2)³ + 3(-2)² + 2(-2) - 2a + b = 15.

→ - 40 + 12 - 4 - 2a + b = 15.

→ - 44 + 12 - 2a + b = 15.

→ - 32 - 2a + b = 15.

→ - 2a + b = 15 + 32.

→ - 2a + b = 47 .......... (4).

Put the value of a = 3b - 36 in equation (4)

we get,

→ - 2 [ 3b - 36 ] + b = 47.

→ - 6b + 72 + b = 47.

→ - 5b = 47 - 72.

→ - 5b = - 25.

→ b = 5.

Put the value of b = 5 in equation (3)

we get,

→ 3(5) - 36 = a.

→ 15 - 36 = a.

→ a = - 21

Value of A = -21 and B = 5.