Choose the correct statement about the nature and value of the roots of \\(16x^2+24x+9=0\\).
Answer and explanation
Correct answer: The roots are real and equal; \\(x=-\frac{3}{4}\\)
Here, \\(a=16, b=24, c=9\\). The discriminant is \\(D=b^2-4ac=24^2-4(16)(9)=0\\), so the roots are real and equal. Also, \\(16x^2+24x+9=(4x+3)^2\\), which gives \\(4x+3=0\\) and hence the equal root \\(x=-\frac{3}{4}\\). Therefore, option B has the wrong sign, while option C gives an incorrect discriminant. Exam tip: If a quadratic is a perfect square or its discriminant is zero, its roots are equal.
Frequently asked questions
What is the correct answer to this question?
The roots are real and equal; \\(x=-\frac{3}{4}\\)
Why is this the correct answer?
Here, \\(a=16, b=24, c=9\\). The discriminant is \\(D=b^2-4ac=24^2-4(16)(9)=0\\), so the roots are real and equal. Also, \\(16x^2+24x+9=(4x+3)^2\\), which gives \\(4x+3=0\\) and hence the equal root \\(x=-\frac{3}{4}\\). Therefore, option B has the wrong sign, while option C gives an incorrect discriminant. Exam tip: If a quadratic is a perfect square or its discriminant is zero, its roots are equal.
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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