Question

Find the discriminant of the following equation x2+5x-6= 0​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Equation is}\;\mathsf{x^2+5x-6=0}$

$\underline{\textsf{To find:}}$

$\textsf{Discriminant of the given quadratic equation}$

$\underline{\textsf{Solution:}}$

$\mathsf{Concept:}$

$\mathsf{The\;discriminant\;of\;the\;quadratic\;equation\;ax^2+bx+c=0\;is\;\boxed{\bf\triangle=b^2-4ac}}$

$\mathsf{Consider,\;x^2+5x-6=0}$

$\mathsf{Here,\;a=1,\;b=5,\;c=-6}$

$\mathsf{Now,}$

$\mathsf{\triangle=b^2-4ac}$

$\mathsf{\triangle=5^2-4{\times}1{\times}(-6)}$

$\mathsf{\triangle=25+24}$

$\mathsf{\triangle=49,\;a\;perfect\;square}$

$\therefore\textsf{Roots are real and rational}$

$\underline{\textsf{Find more:}}$

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Answer 2

Given :- Find the discriminant of the following equation x² + 5x - 6 = 0 ?

Solution :-

we know that,

If A•x^2 + B•x + C = 0 ,is any quadratic equation,

then its discriminant is given by :-

• D = B^2 - 4•A•C

So, comparing given equation x² + 5x - 6 = 0, with A•x^2 + B•x + C = 0 , we get,

• A = 1
• B = 5
• C = (-6)

Putting values we get,

→ D = B² - 4AC

→ D = (5)² - 4 * 1 * (-6)

→ D = 25 - (-24)

→ D = 25 + 24

→ D = 49 (Ans.)

Hence, discriminant of the given equation is 49.

Extra :-

• If D = 0 , then the given quadratic equation has real and equal roots.
• If D > 0 , then the given quadratic equation has real and distinct roots.
• If D < 0 , then the given quadratic equation has unreal (imaginary) roots...

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