Question

please need this answer fast​

Answer 1

Step-by-step explanation:

Let p(x) = 2x3 +3x2 + ax + b

As we know by Remainder Theorem,

If a polynomial p(x) is divided by a linear polynomial (x – a) then, the remainder is p(a)

⇒ Remainder of p(x) when divided by x – 2 is p(2)

p(2) = 2(2)3 +3(2)2 + a(2) + b

⇒ p(2) = 16 + 12 + 2a + b

Also, it is given that p(2) = 2, on substituting value above, wev get,

2 = 28 + 2a + b

⇒ 2a + b = –26 ---------- (A)

Similarly,

Remainder of p(x) when divided by x + 2 is p(–2)

p(–2) = 2(–2)3 +3(–2)2 + a(–2) + b

⇒ p(–2) = –16 + 12 – 2a + b

Also, it is given that p(–2) = –2, on substituting value above, we get,

–2 = –4 – 2a + b

⇒ – 2a + b = 2 ---------- (B)

On solving the above two equ. (A) and (b), we get,

a = –7 and b = –12

∴ Value of a and b is –7 and –12 respectively.