Question

alpha and beta are two zeros of the quadratic polynomial 2xSquare +5x+k and alpha +beta + alpha beta = - 2 find the value of k . ( answer is 1)​

Answer 1

Answer:

k = 1

Step-by-step explanation:

$2x^{2} + 5x + k = 0\\Here \ a \ =2; \ b = 5; \ c = k\\\alpha \ + \ \beta = \frac{-b}{a} = \frac{-5}{2}...(i)\\Also\\\alpha\beta = \frac{c}{a} = \frac{k}{2}...(ii)\\Now \ according \ to \ the \ question\\\alpha + \beta + \alpha\beta =-2\\(\alpha + \beta) + \alpha\beta =-2\\\frac{-5}{2} + \frac{k}{2} = -2...using \ (i) \ and \ (ii)\\\frac{-5 \ + \ k}{2} = -2 \\-5 + k = -4\\k = -4 + 5\\k = 1$

therefore k = 1