Which root nature is correct for 2x² − 5√2x + 12 = 0?
Answer and explanation
Correct answer: No real roots (D = −46).
For a quadratic equation ax²+bx+c=0, the discriminant D=b²−4ac determines the nature of its roots. Here a=2, b=−5√2, and c=12. Thus b²=(−5√2)²=25×2=50, while 4ac=4×2×12=96. Therefore D=50−96=−46. Since the discriminant is negative, the equation has no real roots; its two roots are complex conjugates. Hence option A is correct. D=0 would indicate equal real roots, a positive discriminant would indicate two distinct real roots, and the values D=50 or D=2 are simply incorrect calculations. The irrational coefficient does not change the discriminant rule.
Frequently asked questions
What is the correct answer to this question?
No real roots (D = −46).
Why is this the correct answer?
For a quadratic equation ax²+bx+c=0, the discriminant D=b²−4ac determines the nature of its roots. Here a=2, b=−5√2, and c=12. Thus b²=(−5√2)²=25×2=50, while 4ac=4×2×12=96. Therefore D=50−96=−46. Since the discriminant is negative, the equation has no real roots; its two roots are complex conjugates. Hence option A is correct. D=0 would indicate equal real roots, a positive discriminant would indicate two distinct real roots, and the values D=50 or D=2 are simply incorrect calculations. The irrational coefficient does not change the discriminant rule.
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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