CBSE Class 9 Answered

Class 9 Srijan Mathematics Ex-3.3 Q10 (a,b) Ans- 10/a -. 144 10/b -. -105/4 please Show All The Process

Asked by anikk659 | 08 Jan, 2023, 03:41: PM

Expert Answer

Qn.(10)

begin mathsize 14px style f left parenthesis x right parenthesis space equals space x to the power of 4 space minus space 2 space x cubed minus 13 space x squared minus alpha space x space plus space beta end style

if f(x) is divided by (x-1) , then we get remainder 24

Hence f(1) = 1 -2 -13 -α + β = 24 or - α + β = 38 .................................(1)

if f(x) is divided by (x+2) , then we get remainder -24

Hence f(-2) = 16 +16 -52 + 2α + β = -24 or 2 α + β = -4 .................................(2)

By solving eqn.(1) and (2) , we get α = -14 and β = 24

if f(x) is divided by (x+4) , then we get remainder as

f(4) = 256 +128 -208 +4 α + β = 176 + 4( -14 ) + 24 = 144

Hence, if f(x) is divided by (x+4) , then remainder is 144

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Qn.(11)

begin mathsize 14px style f left parenthesis x right parenthesis space equals space x to the power of 4 space minus space 3 space x cubed minus 27 over 4 space x squared space plus space a space x space minus space b end style

if f(x) is divided by (x-2) , then we get remainder -10

Hence f(2) = 16 +24 - (27/4)4 + 2 a - b = -10 or 2a - b = -23 .................................(3)

if f(x) is divided by (x+4) , then we get remainder 308

Hence f(-4) = 256 + 192 -108 -4a - b = 308 or -4a -b = -32 .................................(4)

By solving eqn.(3) and (4) , we get a = 3/2 and b = 26

if f(x) is divided by (x-3) , then we get remainder as

f(3) = 81 -81 -(27/4)9 + 3(3/2) - 26 = -329 / 4

Hence, if f(x) is divided by (x-3) , then remainder is -329/4

Answered by Thiyagarajan K | 08 Jan, 2023, 09:20: PM

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