What is the nature of the roots of 2x² + 3x − 5 = 0?
Answer and explanation
Correct answer: Two real, rational and distinct (D=49)
For 2x²+3x−5=0, identify a=2, b=3 and c=−5. The discriminant is D=b²−4ac=3²−4(2)(−5)=9+40=49. Since D is positive, the roots are real and distinct. Since 49 is a perfect square, the square root in the quadratic formula is rational, so both roots are rational. Directly, x=[−3±√49]/(2·2)=[−3±7]/4, which gives x=1 and x=−5/2. Thus option A is fully correct. Option B would require D=0, option C would require a negative discriminant, and option D is wrong because D=7 is not the calculated value and the roots are rational rather than irrational.
Frequently asked questions
What is the correct answer to this question?
Two real, rational and distinct (D=49)
Why is this the correct answer?
For 2x²+3x−5=0, identify a=2, b=3 and c=−5. The discriminant is D=b²−4ac=3²−4(2)(−5)=9+40=49. Since D is positive, the roots are real and distinct. Since 49 is a perfect square, the square root in the quadratic formula is rational, so both roots are rational. Directly, x=[−3±√49]/(2·2)=[−3±7]/4, which gives x=1 and x=−5/2. Thus option A is fully correct. Option B would require D=0, option C would require a negative discriminant, and option D is wrong because D=7 is not the calculated value and the roots are rational rather than irrational.
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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