Question

Radhika’s mother gave her some money to buy Papaya from the market at
the rate of p(x) = x² – 12x – 220 per kg.
(i) Find the factors of the given polynomial.
(ii) if she purchase 5kg papaya, what money she have to pay?

Answer 1

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Answer 2

Given: Rate of papaya⇒ p(x)= $x^{2}$ - $12x$ - 220

To find: i) Factors of the polynomial
            ii) Price of 5 kg Papaya.

Solution:

i) $x^{2} -12x-220=0$

⇒ $x^{2} -(22x-10x)-220=0$

⇒ $x^{2} -22x+10x-220=0$

⇒ $x( x-22)+10(x-22)=0$

⇒ $(x-22)(x+10)=0$

∴ The factors of the polynomial are (x-22) and (x+10).

ii) By solving the factors of the polynomial, we get,

x - 22 = 0                                      x + 10 = 0

⇒ x = 22                                       ⇒ x = -10

∵ (x + 10) gives negative answer, we will disregard that.

∴ Price of 1 kg of papaya= ₹ 22

∴ Price of 5 kg of papaya= ₹ (5 $\times$ 22)

                                         = ₹ 110

Answer: i) (x + 10) and (x - 22) are the factors of the polynomial.

             ii) The price of 5 kg papaya is ₹ 110.