Question

find the desriminant of the following and hence find the nature of roots 16 X square - 40 X + 25 equal to zero

Answer 1

$\large{\underline{\bf{\purple{Given:-}}}}$

• p(x)= 16x² - 40x +25

$\large{\underline{\bf{\purple{To\:Find:-}}}}$

• Nature of roots .
• Discriminant

$\huge{\underline{\bf{\red{Solution:-}}}}$

➝ D = b²- 4ac

• a = 16
• b = -40
• c = 25

➝ D = -40² -4 × 16× 25

➝ D = 1600 - 4 × 400

➝ D = 1600 - 1600

➝ D = 0

So the equation have two real and equal roots.

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Extra information:-

➝ D > 0

Nature of roots :- Real and unequal .

Roots :- $\bf\frac{-b\pm\:\sqrt{D}}{2a}$

➝ D = 0

Nature of roots :- Real and equal

Roots:-$\bf\frac{-b}{2a}$

➝ D <0

Nature of roots :- No real roots

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Answer 2

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{The \ value \ of \ Discriminant \ is \ 0}$

$\sf{and \ roots \ are \ real \ and \ equal.}$

$\sf\blue{Explanation:}$

$\sf{Determinant=b^{2}-4ac}$

$\sf{If, \Delta>0, \ Roots \ are \ real \ and \ distinct.}$

$\sf{\Delta=0, \ Roots \ are \ real \ and \ equal.}$

$\sf{\Delta<0, \ Roots \ are \ not \ real.}$

$\sf\orange{Given:}$

$\sf{The \ given \ quadratic \ equation \ is}$

$\sf{\implies{16x^{2}-40x+25=0}}$

$\sf\pink{To \ find:}$

$\sf{Discriminant \ and \ nature \ of \ roots.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{The \ given \ quadratic \ equation \ is}$

$\sf{\implies{16x^{2}-40x+25=0}}$

$\sf{Here, \ a=16, \ b=-40 \ and \ c=25}$

$\sf{Discriminant (\Delta)=b^{2}-4ac}$

$\sf{\Delta=-40^{2}-4(16)(25)}$

$\sf{\Delta=1600-1600}$

$\sf{\Delta=0}$

$\sf\purple{\tt{\therefore{The \ value \ of \ Discriminant \ is \ 0}}}$

$\sf\purple{\tt{and \ roots \ are \ real \ and \ equal.}}$