If the sum of the roots of the quadratic equation 3x^2 + (2k + 1) x – (k + 5) = 0 is equal to the product
If the sum of the roots of the quadratic equation 3x2 + (2k + 1) x – (k + 5) = 0 is equal to the product of the roots, then the value of ‘k’ is
A) 0
B) 1
C) -4
D) 4
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2 Answers
Correct option is (D) 4
Given quadratic equation is
\(3x^2+ (2k + 1)\,x \,– (k + 5)= 0\)
\(\therefore\) Sum of roots \(=\frac{-(2k+1)}3\)
& Product of roots \(=\frac{-(k+5)}3\)
Given that sum of roots = Product of roots
\(\therefore\) \(\frac{-(2k+1)}3\) \(=\frac{-(k+5)}3\)
\(\Rightarrow-(2k+1)=-(k+5)\)
\(\Rightarrow2k+1=k+5\)
\(\Rightarrow2k-k=5-1\)
\(\Rightarrow k=4\)
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