If the two possible values of the discriminant of a quadratic equation are \\(D_1=(y+5)^2\\) and \\(D_2=-(y+5)^2\\), with \\(y\neq -5\\), which case gives two distinct real roots?
Answer and explanation
Correct answer: \\(D_1=(y+5)^2\\)
Since \\(y\neq -5\\), we have \\(y+5\neq 0\\), so \\(D_1=(y+5)^2>0\\). A quadratic equation has two distinct real roots when its discriminant satisfies \\(D>0\\). In contrast, \\(D_2=-(y+5)^2<0\\), which gives no real roots. Exam tip: Check the sign of the discriminant first to determine the nature of the roots.
Frequently asked questions
What is the correct answer to this question?
\\(D_1=(y+5)^2\\)
Why is this the correct answer?
Since \\(y\neq -5\\), we have \\(y+5\neq 0\\), so \\(D_1=(y+5)^2>0\\). A quadratic equation has two distinct real roots when its discriminant satisfies \\(D>0\\). In contrast, \\(D_2=-(y+5)^2<0\\), which gives no real roots. Exam tip: Check the sign of the discriminant first to determine the nature of the roots.
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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