Question

2 Find the value of K, in quadratic equation − + = the rootes are equal ​

Answer 1

Answer:

10th

Maths

Quadratic Equations

Nature of Roots

Find the value of k for whi...

MATHS

Find the value of k for which the quadratic equation (k−2)x

2

+(2k−3)x+(5k−6)=0 has equal roots.

HARD

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ANSWER

Given the equation has equal roots

⇒Discriminant=Δ=b

2

−4ac=0

⇒(2k−3)

2

−4×(k−2)(5k−6)=0

⇒4k

2

+9−12k−4(5k

2

−6k−10k+12)=0

⇒4k

2

+9−12k−4(5k

2

−16k+12)=0

⇒4k

2

+9−12k−20k

2

+64k−48=0

⇒−16k

2

+52k−39=0

⇒16k

2

−52k+39=0

⇒(4k)

2

−2×4k×

2

13

+

4

169

−

4

169

+39=0

⇒(4k−

2

13

)

2

=

4

169

−39

⇒(4k−

2

13

)

2

=

4

169−156

⇒(4k−

2

13

)

2

=

4

13

⇒4k−

2

13

=±

2

13

⇒4k=

2

13±

13

∴k=

8

13±

13