If the value of the polynomial x3-2 x2-a x-1 at x-2 is 11 - find a-

Let #160;px=x3+2x2 ax+1Then #160;p2=23+222 a2+1 #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #1 ...

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Standard VII

Mathematics

Finding the Value of an Expression

If the value ...

Question

If the value of the polynomial x³ + 2x² $-$ ax + 1 at x = 2 is 11, find a.

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Solution

$Let p (x) = x^{3} + 2 x^{2} - a x + 1 Then p (2) = 2^{3} + 2 {(2)}^{2} - a (2) + 1 = 8 + 8 - 2 a + 1 ∴ p (2) = - 2 a + 17 But p (2) = 11 (Given) Now, - 2 a + 17 = 11 \Rightarrow - 2 a = 11 - 17 \Rightarrow - 2 a = - 6 ∴ a = 3$

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If the value of the polynomial x3 + 2x2 - ax + 1 at x = 2 is 11, find a.

Let px=x3+2x2-ax+1Then p2=23+222-a2+1 =8+8-2a+1∴p2=-2a+17But p2=11 GivenNow, -2a+17=11⇒-2a=11-17⇒-2a=-6∴ a = 3

If the value of the polynomial x³ + 2x² $-$ ax + 1 at x = 2 is 11, find a.

$Let p (x) = x^{3} + 2 x^{2} - a x + 1 Then p (2) = 2^{3} + 2 {(2)}^{2} - a (2) + 1 = 8 + 8 - 2 a + 1 ∴ p (2) = - 2 a + 17 But p (2) = 11 (Given) Now, - 2 a + 17 = 11 \Rightarrow - 2 a = 11 - 17 \Rightarrow - 2 a = - 6 ∴ a = 3$