Math, asked by sivamthapa25, 9 months ago

If α and β are the zeroes of the polynomial x² + 5x - 14, find the value of α² + β² (

Answers

Answered by yogeshwarkrishn
28

Answer:

53

Step-by-step explanation:

(α+β)²=α²+β²+2αβ

So

α²+β²=(α+β)²-2αβ

we know that

(α+β)=  -b/a = -5

(α+β)²= 25                                      (1)

and

αβ= c/a = -14

2αβ= -28                                       (2)

now from (1)-(2)

25-(-28)=25+28 = 53

Answered by lifekiller05
14

\huge{\bf{\underline{\underline{\pink{Question}}}}}

If α and β are the zeroes of the polynomial x² + 5x - 14, find the value of α² + β²

\huge{\bf{\underline{\underline{\red{ANSWER}}}}}

we \: know \: that,

( \alpha  +  \beta )^{2} =  \alpha ^{2} +  \beta^{2} + 2 \alpha  \beta

so, \\   { \alpha }^{2} +  { \beta }^{2}  = ( \alpha+ \beta)^{2} - 2 \alpha  \beta

we \: also \: know \: that \: for \: sum \:  of \: \\  zero \: for \: any \:  quadratic \: \\  polynomial : \:  ( \alpha  +  \beta ) =  \frac{ - b}{a}

= -5

 {( \alpha  +  \beta )}^{2} </p><p>= 25...(1)

we \: also \: know \: that \: for \: any \:  \\ qudratic \: polynomial \: product \: of \\ zero \: is : ( \alpha  \beta ) =\frac{ c}{a}

=-14

2 \alpha  \beta  = -  28.... (2)[/tex]

now \: from \: 1^{st} and \: 2^{nd}

 \implies25 - ( - 28) \\ \implies \: \:  \:  \:  25  + 28 \\ \implies \: \: 53

hope \: its \: help \: u.

Similar questions