Which of the following equations has two real, rational and distinct roots?
Answer and explanation
Correct answer: x²−17x+72=0
For ax²+bx+c=0, two real, rational and distinct roots require D=b²−4ac to be positive and a perfect square. For option A, D=(-17)²−4(1)(72)=289−288=1. Since D=1 is positive and a perfect square, the roots are real, distinct, and rational; in fact, they are (17±1)/2, namely 8 and 9. For option B, D=289−320=-31, so there are no real roots. Option C also has D=-31 and therefore no real roots. In option D, D=(-18)²−4(81)=324−324=0, so the roots are real and equal, not distinct. Hence option A is the only correct choice.
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What is the correct answer to this question?
x²−17x+72=0
Why is this the correct answer?
For ax²+bx+c=0, two real, rational and distinct roots require D=b²−4ac to be positive and a perfect square. For option A, D=(-17)²−4(1)(72)=289−288=1. Since D=1 is positive and a perfect square, the roots are real, distinct, and rational; in fact, they are (17±1)/2, namely 8 and 9. For option B, D=289−320=-31, so there are no real roots. Option C also has D=-31 and therefore no real roots. In option D, D=(-18)²−4(81)=324−324=0, so the roots are real and equal, not distinct. Hence option A is the only correct choice.
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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