Question

if α and β are zeroes of the polynomial 2x2+7x-3, then the value of α2+β​​​​​​​2 is

Answer 1

Answer:

α²+β² = 61/4

Explanation:

Compare 2x²+7x-3 with ax²+bx+c , we get

a=2 , b = 7 , c = -3

Now ,

i ) α+β = -b/a = -7/2

ii )αβ = c/a = (-3)/2

α²+β² = (α+β)² - 2αβ

= (-7/2)² - 2(-3/2)

= 49/4 + 3/1

= (49+12)/4

= 61/4

Therefore,

α²+β² = 61/4

••••

Answer 2

$\bf\huge\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

$\bf\huge\bf\huge{\boxed{\bigstar{{2x^2 + 7x - 3 }}}}$        

Here we have

a = 2 , b = 7 , c = -3

Now ,

Sum of Zeroes

α + β ${\implies\dfrac{-b}{a} = \dfrac{-7}{2}}$        

Product of Zero

αβ  ${\implies\dfrac{c}{a} = \dfrac{-3}{2}}$        

Using Formula we get

α² + β² = (α + β)² - 2αβ

${\implies(\dfrac{-7}{2})^2 - 2\times\dfrac{-3}{2}}$        

${\implies\dfrac{49}{4} + \dfrac{3}{1}}$        

${\implies\dfrac{49 + 12}{4}}$  

${\implies\dfrac{61}{4}}$