Question

If alpha and beta are the zeros of polynomial p of x = x square - 3 x minus 2 find the value of alpha / beta + beta / answer

Answer 1

Given :-

${p(x) = x^2-3x-2}$

To find :-

${\huge{\frac{</strong><strong>a</strong><strong>}{</strong><strong>b</strong><strong>}}}$ + ${\huge{\frac{</strong><strong>b</strong><strong>}{</strong><strong>a</strong><strong>}}}$

-» ${\huge{\frac{</strong><strong>a</strong><strong>^</strong><strong>2</strong><strong>+</strong><strong>b</strong><strong>^</strong><strong>2</strong><strong>}{</strong><strong>ab</strong><strong>}}}$

-» ${\huge{\frac{</strong><strong>{</strong><strong>(</strong><strong>a</strong><strong>+</strong><strong>b</strong><strong>)</strong><strong>}</strong><strong>^</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong>-</strong><strong>2ab</strong><strong>}{</strong><strong>ab</strong><strong>}}}$ .......(1)

Proof :-

From the equation,

Sum of roots (a+b) = 3

Product of roots (ab) = -2

Now substitute these in eq (1)

${\huge{\frac{</strong><strong>{</strong><strong>(</strong><strong>3</strong><strong>)</strong><strong>}</strong><strong>^</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong>-</strong><strong>2</strong><strong>(</strong><strong>-</strong><strong>2</strong><strong>)</strong><strong>}{</strong><strong>-</strong><strong>2</strong><strong>}}}$

-» ${\huge{\frac{</strong><strong>9</strong><strong>+</strong><strong>4</strong><strong>}{</strong><strong>-</strong><strong>2</strong><strong>}}}$

-» ${\huge{\frac{</strong><strong>-</strong><strong>1</strong><strong>3</strong><strong>}{</strong><strong>2</strong><strong>}}}$

Thank You.