Given: Rate of papaya⇒ p(x)= [tex]x^{2}[/tex] - [tex]12x[/tex] - 220
To find: i) Factors of the polynomial ii) Price of 5 kg Papaya.
Solution:
i) [tex]x^{2} -12x-220=0[/tex]
⇒ [tex]x^{2} -(22x-10x)-220=0[/tex]
⇒ [tex]x^{2} -22x+10x-220=0[/tex]
⇒ [tex]x( x-22)+10(x-22)=0[/tex]
⇒ [tex](x-22)(x+10)=0[/tex]
∴ 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 [tex]\times[/tex] 22)
= ₹ 110
Answer: i) (x + 10) and (x - 22) are the factors of the polynomial.
ii) The price of 5 kg papaya is ₹ 110.