Which statement is correct for 4x² − 4x + 1 = 0?
Answer and explanation
Correct answer: Roots are equal and x=1/2
The standard form is ax²+bx+c=0, so here a=4, b=−4 and c=1. The discriminant is D=b²−4ac=(−4)²−4(4)(1)=16−16=0. A zero discriminant means that the two roots are real and equal. The equation also factors as 4x²−4x+1=(2x−1)², so 2x−1=0 and the repeated root is x=1/2. Therefore option A gives both the correct nature and the correct value. Option B incorrectly states D=4 and distinct roots; option C contradicts D=0 because real repeated roots exist; and option D uses an incorrect discriminant and incorrectly calls the root irrational. The factorisation independently confirms the discriminant result.
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What is the correct answer to this question?
Roots are equal and x=1/2
Why is this the correct answer?
The standard form is ax²+bx+c=0, so here a=4, b=−4 and c=1. The discriminant is D=b²−4ac=(−4)²−4(4)(1)=16−16=0. A zero discriminant means that the two roots are real and equal. The equation also factors as 4x²−4x+1=(2x−1)², so 2x−1=0 and the repeated root is x=1/2. Therefore option A gives both the correct nature and the correct value. Option B incorrectly states D=4 and distinct roots; option C contradicts D=0 because real repeated roots exist; and option D uses an incorrect discriminant and incorrectly calls the root irrational. The factorisation independently confirms the discriminant result.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
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