First slide

Theory of equations

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

Moderate

A

$8, - 1$
B

$- 9, 2$
C

$- 8, - 2$
D

$9, 1$

Solution

8, 2 are the roots of $x^{2} + αx + β = 0$
$∴ 8 + 2 = 10 = - a, 8.2 = 16 = β i . e . α = - 10, β = 16$
3, 3 are the roots of $x^{2} + αx + b = 0$
$∴ 3 + 3 = 6 = - α, 3.3 = b i . e . α = - 6, b = 9$
Now, $x^{2} + a x + b = 0 becomes x^{2} - 10 + 9 = 0$
or $(x - 1) (x - 9) = 0 \Rightarrow x = 1, 9 .$

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