The nature of the roots of x square + 4 x + 5 is
Answers
Step-by-step explanation:
Explanation:
\sf{Discriminant=b^{2}-4ac}Discriminant=b
2
−4ac
\sf{If, \ \Delta > 0 \ Roots \ are \ real \ and \ distinct.}If, Δ>0 Roots are real and distinct.
\sf{\Delta=0 \ Roots \ are \ real \ and \ equal.}Δ=0 Roots are real and equal.
\sf{\Delta < 0 \ Roots \ are \ not \ real.}Δ<0 Roots are not real.
\sf\orange{Given:}Given:
\sf{The \ given \ quadratic \ equation \ is}The given quadratic equation is
\sf{\implies{x^{2}-4x+5=0}}⟹x
2
−4x+5=0
\sf\pink{To \ find:}To find:
\sf{Nature \ of \ the \ roots.}Nature of the roots.
\sf\green{\underline{\underline{Solution:}}}
Solution:
\sf{The \ given \ quadratic \ equation \ is}The given quadratic equation is
\sf{\implies{x^{2}-4x+5=0}}⟹x
2
−4x+5=0
\sf{Here, \ a=1, \ b=-4 \ and \ c=5}Here, a=1, b=−4 and c=5
\sf{Discriminant (\Delta)=b^{2}-4ac}Discriminant(Δ)=b
2
−4ac
\sf{\Delta=-4^{2}-4(1)(5)}Δ=−4
2
−4(1)(5)
\sf{\Delta=16-20}Δ=16−20
\sf{\Delta=-4}Δ=−4
\sf{\therefore{\Delta < 0}}∴Δ<0
If a quadratic equation is ax^2 + bx + c = 0, then-
D = b^2 - 4ac is called the discriminant of the quadratic equation,
If D > 0, then, the quadratic equation has two distinct real roots,
If D < 0, then, the quadratic equation has two distinct imaginary roots,
If D = 0, then, the quadratic equation has two real equal roots,