For the quadratic equation \\(4x^2-9x+q=0\\) to have two real and equal roots, what should be the value of \\(q\\)?
Answer and explanation
Correct answer: \\(q=\\frac{81}{16}\\)
A quadratic equation has two real and equal roots when its discriminant satisfies \\(D=b^2-4ac=0\\). Here, \\(a=4, b=-9, c=q\\), so \\(D=(-9)^2-4(4)(q)=81-16q\\). Setting this equal to zero gives \\(q=\\frac{81}{16}\\). Exam tip: for equal roots, immediately use the condition \\(D=0\\).
Frequently asked questions
What is the correct answer to this question?
\\(q=\\frac{81}{16}\\)
Why is this the correct answer?
A quadratic equation has two real and equal roots when its discriminant satisfies \\(D=b^2-4ac=0\\). Here, \\(a=4, b=-9, c=q\\), so \\(D=(-9)^2-4(4)(q)=81-16q\\). Setting this equal to zero gives \\(q=\\frac{81}{16}\\). Exam tip: for equal roots, immediately use the condition \\(D=0\\).
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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