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# Hots Questions - Polynomials - Practice Notes - Class 9

## Class 9: Hots Questions - Polynomials - Practice Notes - Class 9

The document Hots Questions - Polynomials - Practice Notes - Class 9 is a part of Class 9 category.
All you need of Class 9 at this link: Class 9

Q.1. If  p(x) = x2 – 2√2 x + 1, then find  p (2√2) .

Sol. Since, p(x) = x– 2 √2 x + 1

= 4 (2) – 4 (2) + 1 = 8 – 8 + 1 = 1

Q.2. If  a + b + c = 9, and ab + bc + ca = 26, find a+ b2 + c2

Sol. (a + b + c)2 =(a+ b+ c2) + 2 (ab + bc + ca)

⇒ (9)=(a2 + b+ c2) + 2 (26)  = (a+ b2 + c2) + 52

⇒ a2 + b+ c2 =92– 52 = 81– 52 = 29

Q.3. Factorise :

Sol.

Q.4. If a, b, c are all non-zero and a + b + c = 0, prove that

Sol. ∵ a + b + c = 0  ⇒  a3 + b3 + c3 – 3abc = 0
or a+ b+ c3 = 3abc ⇒

Q.5. Prove that (a + b + c)3 – a3 – b3 – c3 = 3(a + b) (b + c) (c + a)
Sol.

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