If y-2 and y-1 are the zero of the polynomial find- 2 y3-5 y2-a y-b- Find values of a and b

By remainder theorem if y = 2 and y = 1 are zeros of the po;unomial 2y3 5y2 +ay +b then we get zero when we substitute y = 1 and y = 2 into the polynomial ...

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Standard IX

Mathematics

Remainder Theorem

If y=2 and y=...

Question

If y=2 and y=1 are the zero of the polynomial find: 2y³-5y² +ay +b . Find values of a and b

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Solution

By remainder theorem if y = 2 and y = 1 are zeros of the po;unomial
2y³-5y² +ay +b then we get zero when we substitute y = 1 and y = 2 into the polynomial.
Substituting y = 1 we get
2(1)³-5(1)²+a(1)+b = 0 => 2-5+a+b=0=>-3+a+b=0 => a+b=3 (1)
Substituting y = 2 we get
2(2)³-5(2)²+a(2)+b = 0=> 2(8)-5(4)+2a+b=0
=> 16-20+2a+b=0 => 2a+b = 4 (2)
Subtract (1) from (2) giving a = 4-3 = 1
so b = 3-a= 3-1=2
Answer: a=1, b=2

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If y=2 and y=1 are the zero of the polynomial find: 2y3 -5y​​​​2 +ay +b . Find values of a and b

If y=2 and y=1 are the zero of the polynomial find: 2y³-5y² +ay +b . Find values of a and b