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Algebra of Roots of Quadratic Equations

If a:b=1:5, t...

Question

If $a : b = 1 : 5,$ then the roots of the equation $a x^{2} - b x + 4 a = 0$ is/are

A

4

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B

1

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C

- 1

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D

5

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Solution

The correct option is B $1$
Given equation $a x^{2} - b x + 4 a = 0$
Now, we know that
$a : b = 1 : 5 \Rightarrow \frac{a}{b} = \frac{1}{5} \Rightarrow b = 5 a$

The sum of coefficients
$= a - b + 4 a = a - 5 a + 4 a = 0$
So, one root is $1$
Now, let the other root be $α$
Product of roots
$α \times 1 = \frac{4 a}{a} \Rightarrow α = 4$

Hence, the roots are $1, 4$

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Algebra of Roots of Quadratic Equations

Standard XII Mathematics

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