Question

Find the value of K for which the equation

x² +5kx +16 = 0 has no real roots


class 10th.

mathematics


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Answer 1

Answer:

Step-by-step explanation:

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Answer 2

$\huge \bf \red{ \mid{ \overline{ \underline{ANSWER}}} \mid}$

$\bf \pink{step \: by \: step \: explanation}$

The given equation is

→ x² + 5kx + 16 = 0

→ D = (5k)² - 4( 1 )( 16 ) = 25k² - 64

→ If the equation has no real roots , then D < 0.

$\bf{ \implies \: {25k}^{2} - 64 < 0 }$

$\bf{ \implies \: {k}^{2} < \frac{64}{25}}$

$\begin{lgathered}\bf{ \implies \: k < \frac{8}{5} } \\ \\ \bf{ \implies \: k > \frac{ - 8}{5}}\end{lgathered}$

Hence, for no real roots ,

$\bf{ \frac{ - 8}{5} < k < \frac{8}{5}}$