Math Problem Solver

1- If a & ẞ are the zeros of the quadratic polynomial f(x) = ax² + bx + c,then find the values of

a) alpha ^ 2 + beta ^ 2

3) 1/alpha + 1/beta

(c) * alpha/beta + beta/alpha

( d) alpha ^ 3 + beta ^ 3

(e) * 1/(a ^ 3) + 1/(beta ^ 3)

( f) (alpha ^ 2)/alpha + (beta ^ 2)/alpha

(g) α⁺ + β4

(h) α²β + β2α

2- If a & ẞ are the zeros of the quadratic polynomial f(x) = 3x2 - 4x + 1, then find a quadratic polynomial whose zeros are alpha/beta * delta

3- If a & ẞ are the zeros of the polynomial whose zeros are quadratic polynomial f(x) = x²-x-6,then find a quadratic alpha + 2beta & 2a + 3β.

4- If a & ẞ are the zeros of the quadratic polynomial f(x) = x²-x-4,then find the values of 1/alpha + 1/beta - alpha*beta

5- If a & ẞ are the zeros of the quadratic polynomial f(x) = kx² + 4x + 4 such that x ^ 2 + beta ^ 2 = 2 ^ 4 , find the value of k.

6- If the sum of the squares of zeros of the polynomial 5x2 3x + kis - 11/25 find the value of k.

7-Find a quadratic polynomial, the sum and product of whose zeroes are - 5 and 3, respectively.

8- Find a quadratic polynomial, whose zeroes are - 4 and 1, respectively.

9- Find the zeroes of the quadratic polynomial 2 + 7x + 10 and verify the relationship between the zeroes and the coefficients.

10- Find the zeroes of the polynomial x² - 3 and verify the relationship between the zeroes and the coefficients.

11- Find the zeroes of the quadratic polynomial 6x2 - 3 - 7x and verify the relationship between the zeroes and the coefficients.

12- Find the zeroes of the quadratic polynomial 3x2 - x -4 and verify the relationship between the zeroes and the coefficients.

13- Find the zeroes of the quadratic polynomial 4x2 - 4x + 1 and verify the relationship between the zeroes and the coefficients.

14- If a & ẞ are the zeros of the quadratic polynomial P(x) = x² - (k+6)x + (2k-1). Find the value of "k" if a + β =αβ.

15- If one zero of the quadratic polynomial ( 2+9) x ^ 2 + 13x + 6a is reciprocal the other. Find the value of a.

16- If a & ẞ are the zeros of the quadratic polynomial x2 - x + k and 3a + 2β = 20. Find the value of k.

17- Find a quadratic polynomial whose zeros are 3 - √5 and 3 + √5.

18- Find a quadratic polynomial whose one zero is 8 and product of zeros is (-56).

19- If one zero of the quadratic polynomial x² - 8x + k exceeds the other by 2, then find the zeros of the polynomial and value of k.

20- If one zero of the quadratic polynomial 3x28x (2k+1) is 7 times the other. Find both zeros and k.

21- If the zeros of quadratic polynomial r ^ 2 + px + q are double the zeros of 2x25x-3, then find p and q.

22- If one zero of the quadratic polynomial 2x²-3xp is 3, find the other zero and the value of p.

23- If a & ẞ are the zeros of the quadratic polynomial 2x2 + 3x - 6, then find the value of :

(a) * alpha ^ 2 + beta ^ 2

1) 1/alpha + 1/beta

(c) * alpha/beta + beta/alpha

(d) a³+β3

(e)

(f ) (alpha ^ 2)/8 + (beta ^ 2)/sigma

(g) * alpha ^ 4 + beta

(h ) alpha ^ 2 * beta + beta ^ 2 * alpha

24- If a & ẞ are the zeros of the quadratic polynomial 2x2 - 5x + 7, then find a quadratic polynomial whose zeros are 1/(2a) * and * 1/(2beta)

25- If a & ẞ are the zeros of the quadratic polynomial x2 – 5x + k such that a - ẞ = 1, find the value of k.