EXERCISE 2.2 1. Find the zeroes of the following quadratic polynomials and verify the relationship the zeroes and the coefficients. @r-21-8 (m) 45-45+1 (m) 6r-3-7x (iv) 4ar- (v) F-15 (vi) 3.r-x-4 2. Find a quadratic polynomial each with the given numbers as the sum and prod zeroes respectively. -1 V. (i) 0, V5 3 1 (i) 1.1 (v) (vi) 4.1 4 4 Division Algorithm for Polynomials know that a cubic polynomial has at most three zeroes. However, if you
Answers
Answer:
x2 - 2x - 8 = 0
x2 - 4x + 2x - 8 = 0
x(x-4) +2(x-4) = 0
(x+2)(x-4) = 0
The zeroes of the given quadratic polynomial are -2 and 4
\\\alpha =-2\\ \beta =4
VERIFICATION
Sum of roots:
\\\alpha+\beta =-2+4=2
\\-\frac{coefficient\ of\ x}{coefficient\ of\ x^{2}}\\ =-\frac{-2}{1}\\ =2\\=\alpha +\beta
Verified
Product of roots:
\\\alpha \beta =-2\times 4=-8
\\\frac{constant\ term}{coefficient\ of\ x^{2}}\\ =\frac{-8}{1}\\ =-8\\=\alpha \beta
Verified
Factorize the equation, we get (x+2)(x−4)
Factorize the equation, we get (x+2)(x−4)So, the value of x
Factorize the equation, we get (x+2)(x−4)So, the value of x 2
Factorize the equation, we get (x+2)(x−4)So, the value of x 2 −2x−8 is zero when x+2=0,x−4=0, i.e., when x=−2 or x=4.
Factorize the equation, we get (x+2)(x−4)So, the value of x 2 −2x−8 is zero when x+2=0,x−4=0, i.e., when x=−2 or x=4.Therefore, the zeros of x
Factorize the equation, we get (x+2)(x−4)So, the value of x 2 −2x−8 is zero when x+2=0,x−4=0, i.e., when x=−2 or x=4.Therefore, the zeros of x 2
Factorize the equation, we get (x+2)(x−4)So, the value of x 2 −2x−8 is zero when x+2=0,x−4=0, i.e., when x=−2 or x=4.Therefore, the zeros of x 2 −2x−8 are -2 and 4.
Factorize the equation, we get (x+2)(x−4)So, the value of x 2 −2x−8 is zero when x+2=0,x−4=0, i.e., when x=−2 or x=4.Therefore, the zeros of x 2 −2x−8 are -2 and 4.−1)
