Question

If kx²-5x+3=0 and 2x²-kx+1=0 have equal discriminants, then find the value of k.

Answer 1

Answer:

ax² +bx+ c =0 and Discriminant for this equation is b²- 4ac. Since it is given that

kx^2-5x+3 =0 and 2x^2-kx+1=0 have equal discriminants,

25- 4(3)k = k² -4(2)(1)

k²+12k-33 =0 has two roots

k = [-12+√12²-4(-33)1]/2 or k = [-12-√12²-4(-33)1]/2

k = [-12+√144+132]/2. or. k = [-12-√144+132]/2

k = [-12+√276]/2 or k = [-12-√276]/2

k = 2[-6+√69]/2. or k = 2[-6-√69]/2

k = [-6+√69] or k = [-6-√69]

So the values of k are -6-√69 and -6+√69.