FORMATION OF THE QUADRATIC EQUATION WITH GIVEN ROOTS WORKSHEET

Problem 1 :

Find the quadratic polynomial whose zeroes are −2 & 3

Solution

Problem 2 :

Find a quadratic polynomial whose zeroes are 2 + √3 and 2 – √3

Solution

Problem 3 :

Frame a quadratic polynomial p(x) whose sum of zeroes is -3 and the product of zeroes is -2/3.

Solution

Problem 4 :

Find a quadratic polynomial whose sum of zeroes is -12 and product is 14.

Solution

Problem 5 :

If the sum of the zeroes of the quadratic polynomial

f(x) = kx² - 2x + 3 is 3

find k.               Solution

Problem 6 :

The sum of the roots of the equation

3x² + kx + 5 = 0

will be equal to the product of its roots.          Solution

Problem 7 :

Find the value of k, given that the product of the roots of the equation

(k + 1)x² + (4k + 3)x + (k – 1) = 0 is 7/2

Solution

Problem 8 :

Form an quadratic polynomial whose roots are 2, and -1/2.

Solution

Problem 9 :

What is an equation whose roots are 5+√2 and 5−√2

Solution

Problem 10 :

Write down the quadratic equation in general form for which sum and product of the roots are given below.

– 7/2 , 5/2

Solution

Problem 11 :

If the product of the zeroes of the polynomial ax² - 6x - 6 is 4, then the value of a is 

a) 2/3       b)  3/2      c)  -3/2     d) -2/3

Problem 1 :

If the sum of the roots of

4x² + kx – 7 = 0 is 3,

Find the value of k.

Solution

Problem 2 :

Find the value of K if the sum of the roots of equation

(2k – 1)x² + (4k – 1) x + (K + 3) = 0 is 5/2

Solution

Problem 3 :

For what value of K the roots of the following equations are equal :

(i)  kx² + 4x + 3 = 0      (ii)  2x² + 5x + k = 0

Solution

Problem 4 :

If the difference of the roots of 6x² – 23x + c = 0 is 5/6, find the value of c

Solution

Problem 5 :

If the difference of the roots of x² – 7x + k – 4 = 0 is 5, find the value of k and the roots.

Solution

Problem 6 :

Find the value of k given that if one root of

9x² – 15x + k = 0

exceeds the other by 3. Also find the roots.

Solution

Problem 7 :

The product of the roots of the equation

(k + 1)x² + (4k + 3)x + (k – 1) = 0

is 7/2

Solution

Problem 8 :

If one zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is

a)  10     b) -10    c) 5    d)  -5

Solution

Problem 9 :

If α, β are the zeroes of polynomial f(x) = x² - p(x + 1) - c then (α + 1)(β + 1) = 

a)  c - 1     b)  1 - c     c)  c     d) 1 + c

Solution

Problem 10 :

If α, β are the zeroes of the polynomial f(x) = x² + x + 1, then 1/α + 1/β = 

a)  1     b)  -1    c) 0    d) none

Solution

Problem 11 :

If one of the zeroes of the quadratic polynomial (k - 1) x² + kx + 1 is -3, then the value of k is

a)  4/3     b)  -4/3    c)  -2/3    d)  2/3

Solution

Problem 1 :

Write a quadratic equation in standard form with solutions, x = -3 and x = 4. Use integers for a, b and c.

Solution

Problem 2 :

Write a quadratic equation in standard form with solutions, x = 2/3 and x = -5. Use integers for a, b and c.

Solution

Problem 3 :

Write an equation of the parabola in intercept form y = a(x - p)(x - q) that has x- intercepts of 9 and 1 and passes through (0, -18).

A) y = -1/2(x - 9)(x - 1)              B) y = -1/2(x + 9)(x + 1)

C) y = -2(x - 9)(x - 1)                 D) y = -2(x + 9)(x + 1)

Solution

Problem 4 :

Write an equation of the parabola in intercept form y = a(x - p)(x - q) that has x- intercepts of 12 and -6 and passes through (14, 4).

A) y = 1/10(x - 12)(x + 6)      B) y = 1/10(x + 12)(x - 6)

C) y = 10(x - 12)(x + 6)         D) y = 10(x + 12)(x - 6)

Solution

Problem 5 :

Determine the equation of a quadratic function given zeros x = 4 and point (3, 2).

Solution

Problem 6 :

Use the intercepts and a point on the graph below to write the equation of the function.

Solution

Problem 7 :

Use the intercepts and a point on the graph below to write the equation of the function.

Solution

Problem 8 :

The sum and product of zeroes of p(x) = 63x² - 7x - 9 are S and P respectively. Find the value of S and P. Find the value of 27S + 14P

a)  -1    b)  1    c)  2    d)  -2

Solution

Problem 9 :

If one zero of the quadratic polynomial 2x² - 8x - m is 5/2, then find the other zero.

a)  1/2    b)  3/2    c)  -3/2    d)  -1/2

Solution