Question

If one of the roots of the equation x2 – 13x + 2n + 5 = 0 is three more than the other, then what is the value of n

Answer 1

$\sf{\purple{[ For \:answer\: refer\: to\: attachment : ]}}$

$\large{\underline{\underline{\red{\tt{\purple{\leadsto } More\:Related \: Information:-}}}}}$

$\bf\purple{\bullet}\:\red{Quadratic\: Equation}$

A equation is said to be a quadratic equation if the highest degree of the variable is 2 .The standard form of a quadratic equation is ax² + bx + c . The equation has two roots , which may be real , equal or complex .

Here's a table :

$\boxed{\begin{tabular}{|c|c|}\cline{1-2}\bf Condition &\bf Nature of Roots \\\cline{1-2} Discriminant>0 & Real Roots \\\cline{1-2} Discriminant=0 & Equal roots \\\cline{1-2} Discriminant < 0 & Complex Roots \\\cline{1-2}\end{tabular}}$

If we say the two roots of the quadratic equation as α & β. Then here's a relation between the roots and co - efficients of the quadratic equation .

$\sf{\green{\purple{\mapsto}\:Sum\:of\:the\:roots:-}}$

$\boxed{\red{\bf\green{\dag}\:\alpha+\beta=\dfrac{-b}{a}}}$

$\sf{\green{\purple{\mapsto}\: Product\:of\:the\:roots:-}}$

$\boxed{\red{\bf\green{\dag}\:\alpha\beta=\dfrac{c}{a}}}$