Question

Does equation x2

+x –5= 0 has distinct real roots?​

Answer 1

$\textbf{Given:}$

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

$\textbf{To find:}$

$\textsf{Whether the given equation has distinct real roots}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{x^2+x-5=0}$

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

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

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

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

$\mathsf{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=1+20}$

$\mathsf{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=21}$

$\implies\mathsf{\triangle\;>\;0}$

$\therefore\textsf{Roots of the given equation are real and distinct}$

$\textbf{Find more:}$

Find the discriminant for the quadratic equation 2(p2+q2) x2 +2(p+q)x + 1 =0. (p is not equal to q).. Also determine the nature of the roots

https://brainly.in/question/18352928

Answer 2

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