Assertion: The graph of the quadratic equation \(2x^2-4x+7=0\) does not intersect the \(x\)-axis. Reason: The discriminant of this equation is \(D=-40\). 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, \(a=2\), \(b=-4\), and \(c=7\). Thus, \(D=b^2-4ac=(-4)^2-4(2)(7)=16-56=-40\). Since \(D<0\), the equation has no real roots; therefore, the parabola \(y=2x^2-4x+7\) does not intersect the \(x\)-axis. Hence, both the assertion and the reason are correct, and the reason explains the assertion. Exam tip: If \(D<0\), the graph has no real point of intersection with 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, \(a=2\), \(b=-4\), and \(c=7\). Thus, \(D=b^2-4ac=(-4)^2-4(2)(7)=16-56=-40\). Since \(D<0\), the equation has no real roots; therefore, the parabola \(y=2x^2-4x+7\) does not intersect the \(x\)-axis. Hence, both the assertion and the reason are correct, and the reason explains the assertion. Exam tip: If \(D<0\), the graph has no real point of intersection with 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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