Saved Bookmarks
| 1. |
(37) Find the zeroes of the quadratic polynomial f(x) = 473x2 - 2 V3x - 2 v3 and verify therelationship between the zeros and the coefficients. |
|
Answer» Answer: Firstly FACTORISE the given polynomial and then put each factor equal to zero to FIND required zeroes and then for verification show that Sum of zeroes = - COEFFICIENT of x/coefficient of x² Product of zeroes = constant TERM/coefficient of x² SOLUTION: Let p(x) = 4√3x² +5x -2√3 4√3x² +8x -3x -2√3 [By splitting the middle term] 4x (√3x +2) - √3(√3x +2) (4x-√3) (√3x +2) To find ZEROS, put p(x)= 0 (4x-√3)= 0 or (√3x +2)= 0 4x = √3 or √3x = -2 x= √3/4 or x = -2/√3 Hence, zeroes of the polynomial are √3/4 and -2/√3. Verification: Sum of zeroes = (√3/4) +(-2/√3) - coefficient of x/coefficient of x² =√3/4 -2/√3 - 5/4√3 = (√3×√3)-(2×4)/4√3 -5/4√3 =(3-8)/4√3 - 5/4√3 =-5/4√3 Product of zeroes = (√3/4) (-2/√3)= -½ constant term/coefficient of x² = -½ -2√3/ 4√3 = -½ -½ = -½ So, the relationship between the zeroes and its coefficients is verified. Step-by-step explanation:
|
|