Question

write quadratic equation with roots 7 and -5​

Answer 1

Answer:

The Correct Answer is $x^{2}$ -2x -35 = 0

Step-by-step explanation:

Let Alpha = 7 and Beta = -5

Alpha + Beta = 2

Alpha X Beta = -35

The required quadratic equation is:

$x^{2}$−(α+β)x+α.β=0

$x^{2}$ - 2x -35 = 0

Answer 2

Given,

Roots $\[ = 7, - 5\]$

Solution,

Quadratic polynomial is

$\[{x^2} - \left( {sum\,of\,roots} \right)x + product\,of\,roots = 0\]$

Sum of roots,

$\[\begin{array}{l} = 7 + \left( { - 5} \right)\\ = 2\end{array}\]$

Product of roots,

$\[\begin{array}{l} = 7 \times \left( { - 5} \right)\\ = - 35\end{array}\]$

Polynomial,

$\[\begin{array}{l}{x^2} - 2x + \left( { - 35} \right) = 0\\ \Rightarrow {x^2} - 2x - 35 = 0\end{array}\]$

Hence the quadratic polynomial is $\[{x^2} - 2x - 35 = 0\]$