Question

6. (i) If x = 2 is one root of the equation (k – 3)x2 –
kx – 8 = 0, find the value of k. Also, find the
other root of the equation.
(ii) If x = 4 is one root of (k + 2)x2 – (5k + 2)x – 4
= 0, find the value of k. Also, find the other
root of the equation.
+​

Answer 1

Answer:

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Step-by-step explanation:

Find value of k.

2x

2

+kx−5=0 & x

2

−3x−4=0

→x

2

−3x−4=0

x

2

−4x+x−4=0

x(x−4)+1(x−4)=0

(x+1)(x−4)=0

x=−1 and x=4

→ one root is common

∴2(−1)

2

+k(−1)−5=0

∴2−k−5=0

∴k=−3

Or

2(4)

2

+k(4)−5=0

∴32+4k−5=0

∴k=

4

−27