Question

Polynomials class 10
guys plz solve the question no
2 and 3 plz solve it step by step ............ waiting for answer

Answer 1

Step-by-step explanation:

(2)

Given Equation is f(x) =  x² + x - p(p + 1)

Zeroes of the polynomial is f(x) = 0.

∴ x² + x - p(p + 1) = 0

It can be written as,

⇒ x² + px - px + x - p(p + 1) = 0

⇒ x² + (p + 1)x - px - p(p + 1) = 0

⇒ x(x + p + 1) - p(x + p + 1) = 0

⇒ (x - p)(x + p + 1) = 0

⇒ x = p, -p - 1

(3)

Given Equation is x² - 3x - m(m + 3).

Zeroes is f(x) = 0

∴ x² - 3x - m(m + 3) = 0

⇒ x² + mx - mx - 3x - m(m + 3) = 0

⇒ x² + mx - (m + 3)x - m(m + 3) = 0

⇒ x(x + m) - (m - 3)(x + m) = 0

⇒ (x - m - 3)(x + m) = 0

⇒ x = m + 3, -m.

Hope it helps!

Answer 2

Answer:

ii) X = P or -(P + 1)

iii) X = -3 and m + 3

Step-by-step explanation:

Answer : 2

$x^2 + x - p ( p + 1) =0$

By Factorisation it would be

⇒ $x^2 + ( p + 1 ) x - px - p + 1 = 0$

⇒ $x ( x - p ) + ( p + 1 ) (x - p) = 0$

⇒ ( x + p + 1) ( x - p ) = 0

The zeroes of the given polynomial is x = p and -(P + 1)

Answer : 3

$x^2 - 3x - m (m +3) = 0$

Factorise :

⇒ $x^2 + mx - (m+3)x- m(m+3) = 0$

⇒ $x(x+m) - (m+3)(x+m) = 0$

⇒ $(x+m) (x-m-3) = 0$

⇒ x = -m and m + 3

Therefore the roots or Zeroes of the given polynomial is -m and m + 3 for x

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