Answer
Verified
390.9k+ views
Hint: If zeroes of the quadratic polynomial are given as $\alpha {\text{ and }}\beta $ then the quadratic polynomial can be written as ${{\text{x}}^2} - \left( {\alpha + \beta } \right){\text{x + }}\alpha \beta $ .Put the value of given zeroes in the formula and you’ll get the answer.
Complete step-by-step answer:
Given, the zeroes of a quadratic polynomial are $2$ and $ - 6$.We have to find the quadratic equation. Let $\alpha {\text{ and }}\beta $ be the zeroes of the polynomial then, $\alpha = 2$ and $\beta = - 6$
Now, the quadratic polynomial is written as ${{\text{x}}^2} - \left( {\alpha + \beta } \right){\text{x + }}\alpha \beta $ --- (i)
We have to find the sum of the zeroes and product of the zeroes.
$
\Rightarrow \alpha + \beta = 2 + \left( { - 6} \right) = - 4 \\
\Rightarrow \alpha \beta = 2 \times \left( { - 6} \right) = - 12 \\
$
Since, $\left[
\left( - \right) \times \left( + \right) = - \\
\left( - \right) + \left( + \right) = - \\ \right]$
Now on putting the above values in eq. (i), we get
$ \Rightarrow $ ${{\text{x}}^2} - \left( { - 4} \right){\text{x + }}\left( { - 12} \right)$ Since $\left[
\left( - \right) \times \left( + \right) = - \\
\left( - \right) + \left( + \right) = - \\ \right]$
On simplifying the equation, we get
$ \Rightarrow {{\text{x}}^2}{\text{ + 4x - 12}}$
Answer- The quadratic equation ${\text{ = }}{{\text{x}}^2}{\text{ + 4x - 12}}$
Note: Zeros of polynomials are the values which when put in the polynomial, make the value of the polynomial equal to zero. Zeroes are also called roots of the polynomial. The quadratic equation has two roots as its degree is also $2$.The quadratic polynomial is written in the form -${{\text{x}}^2} - \left( {{\text{sum of roots}}} \right){\text{x + product of roots}}$.
Complete step-by-step answer:
Given, the zeroes of a quadratic polynomial are $2$ and $ - 6$.We have to find the quadratic equation. Let $\alpha {\text{ and }}\beta $ be the zeroes of the polynomial then, $\alpha = 2$ and $\beta = - 6$
Now, the quadratic polynomial is written as ${{\text{x}}^2} - \left( {\alpha + \beta } \right){\text{x + }}\alpha \beta $ --- (i)
We have to find the sum of the zeroes and product of the zeroes.
$
\Rightarrow \alpha + \beta = 2 + \left( { - 6} \right) = - 4 \\
\Rightarrow \alpha \beta = 2 \times \left( { - 6} \right) = - 12 \\
$
Since, $\left[
\left( - \right) \times \left( + \right) = - \\
\left( - \right) + \left( + \right) = - \\ \right]$
Now on putting the above values in eq. (i), we get
$ \Rightarrow $ ${{\text{x}}^2} - \left( { - 4} \right){\text{x + }}\left( { - 12} \right)$ Since $\left[
\left( - \right) \times \left( + \right) = - \\
\left( - \right) + \left( + \right) = - \\ \right]$
On simplifying the equation, we get
$ \Rightarrow {{\text{x}}^2}{\text{ + 4x - 12}}$
Answer- The quadratic equation ${\text{ = }}{{\text{x}}^2}{\text{ + 4x - 12}}$
Note: Zeros of polynomials are the values which when put in the polynomial, make the value of the polynomial equal to zero. Zeroes are also called roots of the polynomial. The quadratic equation has two roots as its degree is also $2$.The quadratic polynomial is written in the form -${{\text{x}}^2} - \left( {{\text{sum of roots}}} \right){\text{x + product of roots}}$.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Which type of bond is stronger ionic or covalent class 12 chemistry CBSE
What organs are located on the left side of your body class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
When people say No pun intended what does that mea class 8 english CBSE