Question

the quadratic equation whose zero's are 2,-1 is​

Answer 1

Step-by-step explanation:

Form of a quadratic equation whose zeroes

are m , n is

x² - ( m + n ) x + mn = 0

***************************************

Here ,

m = 1 , n = -2

m + n = 1 - 2 = -1

mn = 1 × ( - 2 ) = -2

Therefore ,

Required quadratic equation ,

x² - ( -1 ) x + ( -2 ) = 0

x² + x - 2 = 0

I hope this helps You.

Answer 2

Answer -

» We know that,

quadratic equation = $\pink{x^2 -(\alpha +\beta)x + (\alpha \times \beta)}$

where,

$\alpha \:and\:\beta\:are \:roots\:of\: quadratic\: equation$

» Given

$\alpha = 2\\ \\ \\ \beta = -1$

» Solution-

$by\:putting\:values\:of\:\alpha\:and\:\beta\\ \\ \\ x^2 - [2+(-1)]x + (2 \times-1)\\ \\ \\ = x^2 -x-2 \\ \\ \\ {\boxed{\pink{\therefore\: required\: quadratic\: equation= x^2 -x -2}}}$

Verification-

p(x) = x² -x -2

p(2) = (2)² -(2)-(2)

= 4-2-2

= 4-4

= 0

hence, 2 is a root of p(x)

p(-1) = (-1)²-(-1) -2

= 1+1-2

= 2-2

= 0

hence , -1 is a root of p(x).

Hence, verified.

Extra Information-

$\underline{\sf{Types\ of\ algebric\ expressions:}} \\ \\ \tt On\ the\ basis\ of\ degree \begin{cases} \rightarrow Linear\\ \rightarrow Quadratic \\ \rightarrow Cubic \\ \rightarrow Biquadratic\end{cases} \\ \\ \\ and \\ \\ \\ \bf On\ the\ basis\ of\ variables \begin{cases} \rightarrow One\ Variable\\ \rightarrow Two\ Variable\end{cases}$