Quadratic #7

Algebra Level 2

The value of a a for which one root of the quadratic equation ( a 2 − 5 a + 3 ) x 2 + ( 3 a − 1 ) x + 2 = 0 ( a^2 - 5a + 3 ) x^2 + (3a-1)x + 2 = 0

is twice as large as the other is:

3 2/3 1 4

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Radhesh Sarma by Radhesh Sarma , 22, India

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3 solutions

Pranjal Jain
Feb 23, 2015

Since one root is double the other, product of them will be positive. [ α × 2 α = 2 α 2 ] [\alpha ×2\alpha=2\alpha ^2]

By vieta's formula, C A = 2 a 2 − 5 a + 3 > 0 ⇒ a 2 − 5 a + 3 > 0 \dfrac{C}{A}=\dfrac{2}{a^2-5a+3}>0\\\Rightarrow a^2-5a+3>0

We can see that none of 1 , 3 , 4 1,3,4 satisfies. Thus, 2 3 \dfrac{2}{3}

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Shivam Hinduja
Mar 22, 2015

Simplest answer: Check the value of a for each of the options.

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