Question

If alpha, beta are the zeros of a Quadratic polynomial such that alpha +beta=24,alpha - beta= 8. Find a
Quadradc polynomial having alpha and beta as its zeros.
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Answer 1

Answer:

MATHS

If α and β are zeros of a quadratic polynomial such that α+β=24 and α−β=8 find a quadtratic polynomial having α and

ANSWER

α+β=24

α−β=8

(α−β)

2

=(α+β)

2

−4αβ=8

2

or,24

2

−4αβ=64

or,4αβ=576−64=512

or,αβ=128

⇒x

2

−(α+β)x+αβ=0

or,x

2

−24x+128=0

Hence x

2

−24x+128=0 is the quadratic polynomial for the required condition

Answer 2

Step-by-step explanation:

$\alpha + \beta = 24 \: \: \: \: \: .....(1) \\ \alpha - \beta = 8 \: \: \: ......(2) \\ adding \: eqution(1) \: and \: (2) \\ 2 \alpha = 32 \\ \alpha = \frac{32}{2} \\ \alpha = 16 \: ans \\ putting \: values \: of \: \alpha = 16 \\ \alpha + \beta = 24 \\ = > 16 + \beta = 24 \\ = > \beta = 24 - 16 \\ = > \beta = 8 \\ \\ as \: we \: know \: that \: \alpha + \beta = 16 + 8 = 24 \\ \alpha \beta = 16 \times 8 = 128 \\ \\ {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ {x}^{2} - 24x + 128 = 0$