5. If α, β are zeroes of quadratic polynomial x--(k + 6) x + 2 (2k-1

1.	5. If α, β are zeroes of quadratic polynomial x--(k + 6) x + 2 (2k-1). Find k if2
Answer» Let α and β are zeroes of the polynomial = x² - (k + 6)x + 2(2k –1). On comparing with ax²+bx+c=0a= 1, b= -( k+6) , c = 2(2k –1) Sum of zeroes (α+β)= -b/a = -(-(k+6))/1α+β= (k+6)…………....(1) Product of roots = c/a = 2(2k –1)/1α.β= c/a = 4k -2…………(2) Given: (α+β) = ½(αβ ) (k+6) = ½( 4k -2)[From eq 1 & 2]2 (k +6 )= 4k -22k +12 = 4k -22k -4k = -2 -12-2k = -14k = 14/2 k = 7

5. If α, β are zeroes of quadratic polynomial x--(k + 6) x + 2 (2k-1). Find k if2

Answer»

Let α and β are zeroes of the polynomial = x² - (k + 6)x + 2(2k –1).

On comparing with ax²+bx+c=0a= 1, b= -( k+6) , c = 2(2k –1)

Sum of zeroes (α+β)= -b/a = -(-(k+6))/1α+β= (k+6)…………....(1)

Product of roots = c/a = 2(2k –1)/1α.β= c/a = 4k -2…………(2)

Given: (α+β) = ½(αβ ) (k+6) = ½( 4k -2)[From eq 1 & 2]2 (k +6 )= 4k -22k +12 = 4k -22k -4k = -2 -12-2k = -14k = 14/2

k = 7