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) 3 B) 5 C) 4 D) 2
Answer» Correct option is (C) 4 Let \(\alpha\;and\;\beta\) are roots of equation \(3x^2+(2k+1)\,x-(k+5)=0.\) \(\therefore\) Sum of roots \(=\frac{-(2k+1)}3\) \(\Rightarrow\) \(\alpha+\beta\) \(=\frac{-(2k+1)}3\) _____________(1) And product of roots \(=\frac{-(k+5)}3\) \(\Rightarrow\) \(\alpha\beta\) \(=\frac{-(k+5)}3\) _____________(2) Given that sum of roots = Product of roots \(\Rightarrow\) \(\frac{-(2k+1)}3\) \(=\frac{-(k+5)}3\) \(\Rightarrow\) 2k+1 = k+5 \(\Rightarrow\) 2k - k = 5 - 1 = 4 \(\Rightarrow\) k = 4 Correct option is C) 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) 3 B) 5 C) 4 D) 2

Answer»

Correct option is (C) 4

Let \(\alpha\;and\;\beta\) are roots of equation \(3x^2+(2k+1)\,x-(k+5)=0.\)

\(\therefore\) Sum of roots \(=\frac{-(2k+1)}3\)

\(\Rightarrow\) \(\alpha+\beta\) \(=\frac{-(2k+1)}3\) _____________(1)

And product of roots \(=\frac{-(k+5)}3\)

\(\Rightarrow\) \(\alpha\beta\) \(=\frac{-(k+5)}3\) _____________(2)

Given that sum of roots = Product of roots

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

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

\(\Rightarrow\) 2k - k = 5 - 1 = 4

\(\Rightarrow\) k = 4

Correct option is C) 4