Pankaj’s father gave him some money to buy avocado from the market at the rate of p(x) = x^2 -24x +128. Let α and β are the zeroes of p(x). Based on the above information, answer the following questions.
Answers
SOLUTION
TO DETERMINE
Pankaj's father gave him some money to buy avocado from the market at the rate of p(x) = x² - 24x + 128. Let α, β are the zeroes of p(x).
Based on the above information, answer the following questions.
1) Find the value of α and β, where α < β
(a) -8, -16
(b) 8,15
(c) 8,16
(d) 4,9
2) Find the value of α + β + αβ.
(a) 151
(b) 152
(c) 158
(d) 155
3)The value of p(2) is
(a) 80
(b) 81
(c) 83
(d) 84
EVALUATION
Here the given polynomial is
p(x) = x² - 24x + 128
We now find the zeros of the polynomial
For zero of the polynomial
p(x) = 0
⇒ x² - 24x + 128 = 0
⇒ x² - 16x - 8x + 128 = 0
⇒ ( x - 16 ) ( x - 8 ) = 0
⇒ x = 16 , 8
Since it is given that α and β are the zeroes of p(x) with α < β
So we have α = 8 , β = 16
1) Hence the correct option is (c) 8 , 16
2) α + β + αβ
= 8 + 16 + ( 8 × 16 )
= 24 + 128
= 152
Hence the correct option is (b) 152
3) p(x) = x² - 24x + 128
⇒ p(2) = 2² - 24 × 2 + 128
⇒ p(2) = 4 - 48 + 128
⇒ p(2) = 84
Hence the correct option is (d) 84
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https://brainly.in/question/21062028
2.Find the roots of the quadratic equation 6x2 +5x + 1 =0 by method of completing the squares.
https://brainly.in/question/30446963
3. Write a quadratic equation whose root are -4 and -5
https://brainly.in/question/24154410
Answer:
SOLUTION
TO DETERMINE
Pankaj's father gave him some money to buy avocado from the market at the rate of p(x) = x² - 24x + 128. Let α, β are the zeroes of p(x).
Based on the above information, answer the following questions.
1) Find the value of α and β, where α < β
(a) -8, -16
(b) 8,15
(c) 8,16
(d) 4,9
2) Find the value of α + β + αβ.
(a) 151
(b) 152
(c) 158
(d) 155
3)The value of p(2) is
(a) 80
(b) 81
(c) 83
(d) 84
EVALUATION
Here the given polynomial is
p(x) = x² - 24x + 128
We now find the zeros of the polynomial
For zero of the polynomial
p(x) = 0
⇒ x² - 24x + 128 = 0
⇒ x² - 16x - 8x + 128 = 0
⇒ ( x - 16 ) ( x - 8 ) = 0
⇒ x = 16 , 8
Since it is given that α and β are the zeroes of p(x) with α < β
So we have α = 8 , β = 16
1) Hence the correct option is (c) 8 , 16
2) α + β + αβ
= 8 + 16 + ( 8 × 16 )
= 24 + 128
= 152
Hence the correct option is (b) 152
3) p(x) = x² - 24x + 128
⇒ p(2) = 2² - 24 × 2 + 128
⇒ p(2) = 4 - 48 + 128
⇒ p(2) = 84
Hence the correct option is (d) 84
━━━━━━━━━━━━━━━━
Learn more from Brainly :-
1.1. If 1/2 is a root of the quadratic equation x²-mx-5/4=0 , then the value of m is?
https://brainly.in/question/21062028
2.Find the roots of the quadratic equation 6x2 +5x + 1 =0 by method of completing the squares.
https://brainly.in/question/30446963
3. Write a quadratic equation whose root are -4 and -5
https://brainly.in/question/24154410