Question

One root of a quadratic polynomial x^2+5x+ (2k+1) is reciprocal of the others. Then the value of 'k' is...
a. 0
b. 1
c. 2
d. 0.5​

Answer 1

f ( x ) = x² + 5x + k

f ( x ) = x² + 5x + kLet p and 1/p are two roots of f ( x ) ,

f ( x ) = x² + 5x + kLet p and 1/p are two roots of f ( x ) ,compare f ( x ) with ax² + bx + c

f ( x ) = x² + 5x + kLet p and 1/p are two roots of f ( x ) ,compare f ( x ) with ax² + bx + ca = 1 , b = 5 , c = k

f ( x ) = x² + 5x + kLet p and 1/p are two roots of f ( x ) ,compare f ( x ) with ax² + bx + ca = 1 , b = 5 , c = kproduct of the roots = c/a

f ( x ) = x² + 5x + kLet p and 1/p are two roots of f ( x ) ,compare f ( x ) with ax² + bx + ca = 1 , b = 5 , c = kproduct of the roots = c/ap × 1/p = k / 1

f ( x ) = x² + 5x + kLet p and 1/p are two roots of f ( x ) ,compare f ( x ) with ax² + bx + ca = 1 , b = 5 , c = kproduct of the roots = c/ap × 1/p = k / 11 = k

f ( x ) = x² + 5x + kLet p and 1/p are two roots of f ( x ) ,compare f ( x ) with ax² + bx + ca = 1 , b = 5 , c = kproduct of the roots = c/ap × 1/p = k / 11 = kTherefore ,

f ( x ) = x² + 5x + kLet p and 1/p are two roots of f ( x ) ,compare f ( x ) with ax² + bx + ca = 1 , b = 5 , c = kproduct of the roots = c/ap × 1/p = k / 11 = kTherefore ,value of k = 1

f ( x ) = x² + 5x + kLet p and 1/p are two roots of f ( x ) ,compare f ( x ) with ax² + bx + ca = 1 , b = 5 , c = kproduct of the roots = c/ap × 1/p = k / 11 = kTherefore ,value of k = 1I hope this helps you.

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