The polynomials a xa x 3-3 x2-4 and 2 x3-5 x-a when divided by x-2 leave the remainder p and q respectively-If p-2 q-4- find a

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Standard IX

Mathematics

Factor Theorem

The polynomia...

Question

The polynomials ax^ax3- 3x²+4 and 2x³-5x+a when divided by x-2 leave the remainder p and q respectively.If p-2q=4 , find a

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Solution

p(x)=ax^3-3x^2+4

g(x)=2x^3-5x+a ..

factor of g(x) and p(x) are x-2

p(2)= 8a-12+4=p [Remainder thm.]

= 8a-8=p

g(2)=16-10+a=q

=6+a=q

p-2q=4

8a-8-2(6+a)=4

8a-8-12-2a=4

6a-20=4

6a=24

a=24/6=4

Like if satisfied

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Similar questions

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The polynomials ax​​​​​ax3​​- 3x2+4 and 2x3-5x+a when divided by x-2 leave the remainder p and q respectively.If p-2q=4 , find a

p(x)=ax^3-3x^2+4 g(x)=2x^3-5x+a .. factor of g(x) and p(x) are x-2 p(2)= 8a-12+4=p [Remainder thm.] = 8a-8=p g(2)=16-10+a=q =6+a=q p-2q=4 8a-8-2(6+a)=4 8a-8-12-2a=4 6a-20=4 6a=24 a=24/6=4 Like if satisfied

The polynomials ax^ax3- 3x²+4 and 2x³-5x+a when divided by x-2 leave the remainder p and q respectively.If p-2q=4 , find a

p(x)=ax^3-3x^2+4

g(x)=2x^3-5x+a ..

factor of g(x) and p(x) are x-2

p(2)= 8a-12+4=p [Remainder thm.]

= 8a-8=p

g(2)=16-10+a=q

=6+a=q

p-2q=4

8a-8-2(6+a)=4

8a-8-12-2a=4

6a-20=4

6a=24

a=24/6=4

Like if satisfied