If 8- 2 are the roots of x2-ax-0 and 3- 3 are the roots of x2- x-b-0 - then the roots of x2-ax-b-0 are

8, 2 are the roots of x^2 + ax + β = 0 ∴ nbsp; nbsp;8 + 2 = 10 = –a, 8.2 = 16 = β nbsp; i.e., a = –10, β nbsp;= 16 3, 3 are the roots of x^2 nbsp; ...

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Byju's Answer

Standard XIII

Mathematics

Relations between Roots and Coefficients

If 8, 2 are t...

Question

If 8, 2 are the roots of $x^{2} + a x + β = 0$ and 3, 3 are the roots of $x^{2} + α x + b = 0$ , then the roots of $x^{2} + a x + b = 0$ are

9, 1

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– 9, 2

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-8, -2

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8, - 1

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Solution

The correct option is A
9, 1

8, 2 are the roots of $x^{2} + a x + β = 0$

$∴ 8 + 2 = 10 = - a, 8.2 = 16 = β i . e ., a = - 10, β = 16$

3, 3 are the roots of $x^{2} + α x + b = 0$

$∴ 3 + 3 = 6 = - α, 3.3 = b i . e, α = - 6, b = 9$

Now, $x^{2} + a x + b = 0$ becomes
$x^{2} - 10 x + 9 = 0$

or $(x - 1) (x - 9) = 0 \Rightarrow x = 1, 9$

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If 8, 2 are the roots of $x^{2} + a x + β = 0$ and 3, 3 are the roots of $x^{2} + α x + b = 0$ , then the roots of $x^{2} + a x + b = 0$ are

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If 8, 2 are the roots of x2+ax+β=0 and 3, 3 are the roots of x2+αx+b=0 , then the roots of x2+ax+b=0 are

The correct option is A 9, 1 8, 2 are the roots of x2+ax+β=0 ∴8+2=10= –a,8.2=16=β i.e.,a= –10,β=16 3, 3 are the roots of x2+αx+b=0 ∴3+3=6=−α,3.3=bi.e,α= –6,b=9 Now, x2+ax+b=0 becomes x2–10x+9=0 or (x –1)(x –9)=0⇒x=1,9

If 8, 2 are the roots of $x^{2} + a x + β = 0$ and 3, 3 are the roots of $x^{2} + α x + b = 0$ , then the roots of $x^{2} + a x + b = 0$ are