If the sum of the roots of the quadratic equation 3x2 + (2k + 1) x –

1.	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
Answer» 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 \(\therefore\) \(\frac{-(2k+1)}3\) \(=\frac{-(k+5)}3\) \(\Rightarrow-(2k+1)=-(k+5)\) \(\Rightarrow2k+1=k+5\) \(\Rightarrow2k-k=5-1\) \(\Rightarrow k=4\) Correct option is D) 4

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

Answer»

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

\(\therefore\) \(\frac{-(2k+1)}3\) \(=\frac{-(k+5)}3\)

\(\Rightarrow-(2k+1)=-(k+5)\)

\(\Rightarrow2k+1=k+5\)

\(\Rightarrow2k-k=5-1\)

\(\Rightarrow k=4\)

Correct option is D) 4