Question

x²+5px+16 has no real roots than​

Answer 1

Answer:

Given quadratic equation is=x² + 5px +16 = 0

On comparing with standard form of quadratic equation i.e ax² + bx + c =0,

Here, a = 1 , b= 5p, c= 16

D(discriminant)= b²-4ac

= (5p)² - 4× 1 × 16

= 25p² - 64

Since, roots of given equation has no real roots.  D < 0.

25p² - 64 <0

5p² - 8² < 0

(5p +8)(5p -8)< 0

[ a² - b² = (a-b)(a+b)]

5p +8 <0 or 5p - 8< 0

k > -8/5 or k < 8/5

-8/5 < k  < 8/5

Hence, the required value of k is -8/5 < k  < 8/5.

HOPE THIS WILL HELP YOU...

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