Question

u find the quadratic equations in variable
x whose
roots
are 2 and 5
​

Answer 1

Answer:

I have found the equation that have roots of 2 and 5.

MARK BRAINLY IF USEFUL

Answer 2

$\Huge{\textbf{\textsf{{\purple{Ans}}{\pink{wer}}{\color{pink}{:}}}}}$

Method - 1:

Formula :

$if \: \alpha \: \: and \: \: \beta \: \: are \: the \: zeroes \\ \: / \: roots \: of \: quadratic \: equation \: then \\ \: the \: equation \: is \: \\ \\ {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0</p><p>$

Now,

Here given,

2 and 5 are the zeroes / roots of quadratic equation.

So sum of the roots = 2+5 = 7

products of the roots = 2×5 = 10

So the equation is :

${x}^{2} - (2 + 5)x + 2 \times 5 = 0 \\ \implies \: {x}^{2} - 7x + 10 = 0$

Method -2:

$if \: \: a, \: b, \: \: c, \:-\:d \: ... \: n \: \: are \: the \: roots \: of \: any \\ \: equation \: then \: it \: is \\ \\ (x - a)(x - b)(x - c)(x+d) ...(x - n) = 0 \\ \\so \: if \: 2 \: and \: 5 \: are \: the \: zeroes \: / \: roots \\ of \: quadratic \: equation. \: then \: it \: is \\ (x - 2)(x - 5) = 0 \\ \implies \: {x}^{2} - 5x - 2x + 10 = 0 \\ \implies \: {x}^{2} - 7x + 10 = 0</p><p>$