Question

$3x {}^{2} + 8x - 10 \: \: find \: \: the \: \: value \: \: of \:$
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Answer 1

$\Large\bf3x {}^{2} + 8x - 10$

Here,

• D = b² - 4ac

$\bf \to \: D = {(8)}^{2} - 4(3)(10) \\ \tt \to64 - 120 \\ \tt\to \blue{ - 56}$

We know,

There exist three condition to determine the nature of roots of a Quadratic Equation :-

$1) \: \text{When discriminant is less than zero, } \\ \: \: \: \text{i.e. } \: \rm{}{b}^{2} - 4ac < 0 , \text {then, roots are non-} \\ \: \: \: \text {real numbers.}$

$\rm{}2) \: \text{When discriminant is equal to zero} \\ \: \: \: i.e. \: \rm {b}^{2} - 4ac = 0 \text{ , Then, The roots }\\ \: \: \: \text {are real \& similar.}$

$3) \: \text{When discriminant is more than zero, } \\ \: \: \: \text{i.e. } \: \rm{}{b}^{2} - 4ac > 0 , \text {then, roots are two} \\ \: \: \: \text {distinct and real numbers.}$

Thus,

• 3x² + 8x - 10 has non-real roots as D < 0 i.e. D = -56

So,

• It can't be factorised further.