Question

TRUE OR FALSE Equation x²+5x+8=0 has no real roots.​

Answer 1

Answer:

False it has roots check by that big formula

Answer 2

★ Answer:-

True, x²+5x+8=0 has no real roots.

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★ Explanation:-

To find the nature of roots, we can apply formula of discriminant and nature of roots can be expressed as follows:

$\boxed{\begin{tabular}{c| l}\bf Discriminant&\bf\qquad Nature\\\cline{1-2}\\\sf Negative&\sf No\;real\:roots\\\sf Positive&\sf Two\: distinct\:roots&\sf 0 &\sf Two\:equal\:roots\end {tabular}}$

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We have formula for discriminant:-

${\star\underline{\boxed{\sf D=b^2-4ac}}}$

Here the values of:-

• D=Discriminant

• a=Coefficient of x²

• b=coefficient of x

• c=constant term

So let's apply formula in the given equation!!

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Given quadratic equation:

⇒ x²+5x+8=0

Here:-

a, coefficient of x²=1

b, coefficient of x=5

c, constant term=8

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★ D=b²-4ac

⇒ D=(5)²-4(1)(8)

⇒ D=25-32

⇒ D=-7

Since value of D (discriminant) is negative, this quadratic equation has no roots.

∵ given statement is correct.

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