Assertion: The graph of the parabola \(y=3x^2-6x+11\) does not intersect the \(x\)-axis. Reason: The discriminant of the corresponding quadratic equation is \(D=-96\). Choose the correct option.
Answer and explanation
Correct answer: Both the assertion and the reason are correct, and the reason correctly explains the assertion
Here, \(a=3\), \(b=-6\), and \(c=11\). Thus, the discriminant is \(D=b^2-4ac=(-6)^2-4(3)(11)=36-132=-96\). Since \(D<0\), the equation has no real roots; therefore, the parabola neither intersects nor touches the \(x\)-axis. Hence, both the assertion and the reason are correct, and the reason correctly explains the assertion. Exam tip: \(D<0\) indicates no real intersection between the parabola and the \(x\)-axis.
Frequently asked questions
What is the correct answer to this question?
Both the assertion and the reason are correct, and the reason correctly explains the assertion
Why is this the correct answer?
Here, \(a=3\), \(b=-6\), and \(c=11\). Thus, the discriminant is \(D=b^2-4ac=(-6)^2-4(3)(11)=36-132=-96\). Since \(D<0\), the equation has no real roots; therefore, the parabola neither intersects nor touches the \(x\)-axis. Hence, both the assertion and the reason are correct, and the reason correctly explains the assertion. Exam tip: \(D<0\) indicates no real intersection between the parabola and the \(x\)-axis.
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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