CAT 2019 Shift 2 Paper

Question : 67 of 100

Marks: +1, -0

Section : QA

Let A be a real number. Then the roots of the equation

x^2 - 4x - \log_2A = 0

are real and distinct if and only if

Solution:

For quadratic equation

a x^{2}+b x+c=0,

the roots are real and distinct if

b^{2}-4 a c>0

Given,

x^{2}-4 x-\log _{2} A=0

∴ (-4)^{2}-4 × 1 ×(-\log _{2} A)>0

⇒ 16+4 \log _{2} A>0

⇒ \log _{2} A>-4

⇒ A>2^{-4}

⇒ A>\;{1}/{16}

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