If a and ß are zeroes of the polynomial 2x² + 3x – 6, then find the value of a +B2 – aß.​

Question

If a and ß are zeroes of the polynomial 2x² + 3x – 6, then find the value of a +B2 – aß.​

in progress 0
Brielle 1 month 2021-09-17T09:40:17+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-09-17T09:41:39+00:00

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

    • P(x) = 2x² + 3x – 6
    • α and β are the zeros

    \bold{\blue{\underline{\red{Zeros}\pink{\:of\:}\green{\:the\:Quadratic\:equation}\purple{:-}}}}

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

    \bold{\blue{\underline{\red{General}\pink{\:form \:of }\green{\:Quadratic\:equation}\purple{:-}}}}

    • ax² + bx + c = 0

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

    • To find the value of α + β² – αβ

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

    • 2x² + 3x 6
    • a = 2
    • b = 3
    • c = -6
    • Quadratic formula = \bold{\frac{-b\: \pm\:{\sqrt{b^{2}\:-\:4ac} }}{2a}}  
    • α = \bold{\frac{-3\: \pm\:{\sqrt{3^{2}\:-\:4(2)(-6)} }}{2(3)}}  
    • α = \bold{\frac{-3\: \pm\:{\sqrt{9\:+\:48} }}{6}}  
    • α = \bold{\frac{-3\: +\:{\sqrt{57} }}{6}}
    • β = \bold{\frac{-3\: -\\\:{\sqrt{57} }}{6}}

       To find the value of α + β² – αβ :

    • \bold{\frac{-3\: +\:{\sqrt{57} }}{6}}  +  \bold({\frac{-3\: -\\\:{\sqrt{57} }}{6})}^2   –    \bold{\frac{-3\: +\\\:{\sqrt{57} }}{6}} \: \times\: \bold{\frac{-3\: -\\\:{\sqrt{57} }}{6}}
    • \bold{\frac{-3\: +\:{\sqrt{57} }}{6}}  + \bold{\frac{9\: +\:57 }{36}}\bold{\frac{9\: -\:57 }{36}}
    • \bold{\frac{-3\: -\:\sqrt{57} }{6}}  +  \bold{\frac{18}{36} }
    • \bold{\frac{-3\: -\:\sqrt{57} }{6}} + \bold{\frac{3}{6} }
    • \bold{\frac{-3\: -\:\sqrt{57}\:+\:3 }{6}}
    • \bold{\frac{ -\:\sqrt{57} }{6}}

Leave an answer

Browse
Browse

18:9+8+9*3-7:3-1*13 = ? ( )