Question

What is the nature of the roots of the quadratic equation 2x^3 3x-4=0​

Answer 1

CORRECT QUESTION:

What is the nature of roots of quadratic equation 2x²+3x-4=0?

SOLUTION:

Nature of the roots of any quadratic equation can be find by applying formula of discriminant. Nature of roots can be expressed as follows:-

$\qquad\qquad\quad\large{\sf{Nature\: of\: roots}}\\\\\boxed{\begin{array}{|c||c|}\cline{1-2}\bf{Discriminant}&\bf{Nature}\\\cline{1-2}\sf{+ve}&\sf{2\: distinct\:roots}\\\cline{1-2}\sf{-ve}&\sf{No\:real\:roots}\\\cline{1-2}\sf{0}&\sf{2\: equal\:roots}\cline{1-2}\cline{1-2}\end{array}}$

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In the given quadratic equation:-

a=coefficient of x²=2

b=coefficient of x=3

c=constant term=-4

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We have formula of discriminant:-

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

$\sf{D=3^{2}-4(2)(-4)}$

$\sf{D=9+32}$

$\sf{D=41}$

Here the value of D is +ve, so:-

$\Large{\underline{\boxed{\bf{NATURE}\longrightarrow\sf{2\: distinct\:roots}}}}$

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