Question

find the value of x , if the pairs of rational numbers given below are equivalent 3/7 , x/42

Answer 1

2/7=x/42
7x=84
x=12
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Answer 2

Answer:

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10th

Maths

Quadratic Equations

Nature of Roots

The positive value of k for...

MATHS

The positive value of k for which the equations x

2

+kx+64=0 and x

2

−8x+k=0 will both have real roots is ________.

EASY

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ANSWER

For a quadratic equation to have real roots, discriminant must be greater than or equal to zero.

For the first equation,

k

2

−4(1)(64)≥0 (∵discriminant=b

2

−4ac)

⇒ k

2

−256≥0

⇒ (k−16)(k+16)≥0

⇒ k≥16 and k≤−16

For the second equation,

64−4k≥0

⇒ k≤16

∴ the value of k that satisfies both the conditions is k=16.