Question

19. If a and ß are the zeros of the quadratic polynomial f(x) =x?- 4x+ 3, find the value of
a*82 + a²8*.
​

Answer 1

Answer:

12

Step-by-step explanation:

Polynomials written in form of x^2 - Sx + P, represent S as sum of roots and P as product of roots.

So, here, if a and b are roots,

Sum = a + b = 4

Product = ab = 3

We are said to find-

= > ab² + ba²

= > ab( a + b )

= > product( sum )

= > 3 (4)

= > 12

Answer 2

Required answer:

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This is one of the basic quadratic equation question. First let's know the general form of quadratic polynomial (x² - Sum of x + Product of x).

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Here, α, β are the roots.

• Sum = α + β
• Product = α(β)

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Coming back to the given equation:

$\longrightarrow\rm{a + b = (4).}$

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$\longrightarrow\rm{a (b) = (3).}$

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$\longrightarrow\rm{ab^{2} + ba^{2}}.$

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So,

$\longrightarrow\rm{ab (a + b) = 3 (4)}.$

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${\longrightarrow{\boxed{\rm{12.}}}}$