Which of the following statements is true for the equation \(x^2 - 12x + 40 = 0\)?
Answer and explanation
Correct answer: It has no real roots
Compute the discriminant: \(D=b^2-4ac = (-12)^2 - 4\cdot1\cdot40 = 144 - 160 = -16 < 0\). When \(D<0\) a quadratic has no real roots (the roots are non-real complex conjugates). Thus option A is correct. Option B is wrong because equal (repeated) real roots occur only if \(D=0\). Option C is wrong because two distinct real roots require \(D>0\). Option D is wrong because the product of the roots equals \(c/a = 40\), not \(-40\). Exam tip: always evaluate \(D\) first to decide the nature of roots; use sum = \(-b/a\) and product = \(c/a\) for quick checks.
Frequently asked questions
What is the correct answer to this question?
It has no real roots
Why is this the correct answer?
Compute the discriminant: \(D=b^2-4ac = (-12)^2 - 4\cdot1\cdot40 = 144 - 160 = -16 < 0\). When \(D<0\) a quadratic has no real roots (the roots are non-real complex conjugates). Thus option A is correct. Option B is wrong because equal (repeated) real roots occur only if \(D=0\). Option C is wrong because two distinct real roots require \(D>0\). Option D is wrong because the product of the roots equals \(c/a = 40\), not \(-40\). Exam tip: always evaluate \(D\) first to decide the nature of roots; use sum = \(-b/a\) and product = \(c/a\) for quick checks.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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