Assertion: The graph of x² + 2x + 5 = 0 does not cut the x-axis. Reason: Its discriminant D = −16. Choose the correct option.
Answer and explanation
Correct answer: Both assertion and reason are correct.
The x-intercepts of the parabola y=x²+2x+5 are obtained by solving x²+2x+5=0. Its discriminant is D=b²−4ac=2²−4(1)(5)=4−20=−16. A negative discriminant means the quadratic has no real zeros. Consequently, the graph has no point whose y-coordinate is zero, so it does not meet or cut the x-axis. The assertion is therefore true, and the stated reason is also true and directly explains it. Hence option A is correct. If D were zero, the graph would touch the x-axis once; if D were positive, it would cut the axis at two points. Options B, C, and D incorrectly reject either the assertion, the calculation, or both.
Frequently asked questions
What is the correct answer to this question?
Both assertion and reason are correct.
Why is this the correct answer?
The x-intercepts of the parabola y=x²+2x+5 are obtained by solving x²+2x+5=0. Its discriminant is D=b²−4ac=2²−4(1)(5)=4−20=−16. A negative discriminant means the quadratic has no real zeros. Consequently, the graph has no point whose y-coordinate is zero, so it does not meet or cut the x-axis. The assertion is therefore true, and the stated reason is also true and directly explains it. Hence option A is correct. If D were zero, the graph would touch the x-axis once; if D were positive, it would cut the axis at two points. Options B, C, and D incorrectly reject either the assertion, the calculation, or both.
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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