Question

If a and Bare zeroes of 2x2 -X-6 then the value of 1/ a + 1/B is

Answer 1

$\bold{\blue{\underline{\red{G}\pink{iv}\green{en}\purple{:-}}}}$

• P(x) = 2x² - x - 6

$\bold{\blue{\underline{\red{Zeros}\pink{\:of\:}\green{\:the\:polynomials}\purple{:-}}}}$

• Zeros of the polynomial is the value of the variable for which when replaced in the polynomial the value for the polynomial changes to zero.

$\bold{\blue{\underline{\red{General}\pink{\:form \:of }\green{\:polynomial}\purple{:-}}}}$

• $\bold{a_{n}x^n + a_{n-1}x^{n-1} +...... + a_{2}x^2 + a_{1}x + a_{0}}$
• Where ' $\bold{a_{n} , a_{n-1} ...... a_{1} , a_{0}}$ ' are Real numbers and 'n' is an integer .

$\bold{\blue{\underline{\red{Q}\pink{uest}\green{ion}\purple{:-}}}}$

• To find  $\bold{\frac{1}{\alpha}\:+\:\frac{1}{\beta}}$ . If 'α' and 'β' are the roots of the given equation.

$\bold{\blue{\underline{\red{S}\pink{olut}\green{ion}\purple{:-}}}}$

    $\bold{\blue{\underline{\red{To}\pink{\:find}\green{\:\frac{1}{\alpha} \:and\:\frac{1}{\beta} }\purple{:-}}}}$

• $\bold{\frac{1}{\alpha}\:+\:\frac{1}{\beta}}$

• LCM = αβ

• $\bold{\frac{\beta\:+\:\alpha}{\alpha\beta} }$  ⇒ (i)

    $\bold{\blue{\underline{\red{We}\pink{\:know}\green{\:that}\purple{:-}}}}$

• α + β = $\bold{\frac{-b}{a}}$

• α + β = $\bold{\frac{-(-1)}{2}}$

• α + β = $\bold{\frac{1}{2}}$  ⇒ (ii)

• αβ = $\bold{\frac{c}{a} }$

• αβ = $\bold{\frac{-6}{2} }$  

• αβ = $\bold{-3}$ ⇒ (iii)

• Now, by replacing '(ii)' and '(iii)' in '(i)' we get:

• $\bold{\frac{\beta\:+\:\alpha}{\alpha\beta} }$ =  $\bold{\frac{1}{-3\:\times\: 2}}$  

     SOLUTION   ⇒      $\boxed{\bold{\frac{1}{\alpha}\:+\:\frac{1}{\beta}} \:= \:\bold{\frac{1}{-6}}}$