SUM AND PRODUCT OF THE ROOTS OF A QUADRATIC EQUATION EXAMPLES

About "Sum and product of the roots of a quadratic equation examples"

"Sum and product of the roots of a quadratic equation examples" is nothing but the stuff which explains us few of the relationships between the zeros between coefficients of quadratic equation.

Let us consider the general form of a quadratic equation, 

 ax² + bx + c = 0

(Here a, b and c are real and rational numbers)

Let "α" and "β" be the two zeros of the above quadratic equation. 

Then the formula to get sum and product of the roots of a quadratic equation is,

Examples

To have better understanding on "Sum and product of the roots of a quadratic equation examples", let us look at some sample problems.

Example 1 :

Find the sum and product of roots of the quadratic equation given below.

x² -5x + 6 =0

Solution :

When we compare  the given equation with the general form,  we get a = 1, b = -5 and c = 6.

Sum of the roots = -b/a = -(-5)/1 = 5

Product of the roots = c/a = 6/1 = 6

Example 2 :

Find the sum and product of roots of the quadratic equation given below.

x² - 6 =0

Solution :

When we compare  the given equation with the general form,  we get a = 1, b = 0 and c = -6.

Sum of the roots = -b/a = 0/1 = 0

Product of the roots = c/a = -6/1 = -6

Example 3 :

Find the sum and product of roots of the quadratic equation given below. 

3x² + x + 1 =0

Solution :

When we compare  the given equation with the general form,  we get a = 3, b = 1 and c = 1.

Sum of the roots = -b/a = -1/3

Product of the roots = c/a = 1/3

Example 4 :

Find the sum and product of roots of the quadratic equation given below.

3x² +7x = 2x-5

Solution :

First let us write the given quadratic equation in general form.

3x² +7x = 2x-5 ---------> 3x² + 5x + 5 = 0

Now, the given equation is in general form. If we compare it to the general form, we get  a = 3, b = 5 and c = 5.

Sum of the roots = -b/a = -5/3

Product of the roots = c/a = 5/3

Example 5 :

Find the sum and product of roots of the quadratic equation given below.

3x² -7x + 6 = 5

Solution :

First let us write the given quadratic equation in general form.

3x² -7x +6 = 5 ---------> 3x² - 7x + 1 = 0

Now, the given equation is in general form. If we compare it to the general form, we get  a = 3, b = -7 and c = 1.

Sum of the roots = -b/a = -(-7)/3 = 7/3

Product of the roots = 1/3 = 1/3

Example 6 :

Find the sum and product of roots of the quadratic equation given below.

x² + 5x + 1 = 3x² + 6

Solution :

First let us write the given quadratic equation in general form.

x² + 5x + 1 = 3x² + 6 ---------> 0 = 2x² - 5x + 5

(or)  2x² - 5x + 5 = 0

Now, the given equation is in general form. If we compare it to the general form, we get  a = 2, b = -5 and c = 5.

Sum of the roots = -b/a = -(-5)/2 = 5/2

Product of the roots = 5/2 = 5/2

Now, we are going to look at some quiet different problems on "Sum and product of the roots of a quadratic equation examples"

Example 7 :

If the product of roots of the quadratic equation 2x² + 8x - m³ = 0 is  4, find the value of "m".

Solution :

When we compare  the given equation with the general form,  we get a = 2, b = 8 and c = - m³

Product of the roots = 4 (given)

That is, c/a = 4

-m³/2 = 4

-m³ = 8

m³ = -8

m³ = (-2)³ ----------> m = -2

Example 8 :

If the sum of roots of the quadratic equation

x² - (p+4)x + 5= 0 is  0, find the value of "p".

Solution :

When we compare  the given equation with the general form,  we get a = 1, b = - (p+4) and c = 5

Sum of the roots = 0  (given)

That is,  -b/a  = 0

-[-(p+4)] = 0

p + 4 = 0 ------------> p = - 4

Example 9 :

If the product of roots of the quadratic equation

x² + (2p-1)x + p² = 0  is  1, find the value of "p".

Solution :

When we compare  the given equation with the general form,  we get a = 1, b =  (2p-1) and c = p²

Product of the roots = 1 (given)

That is, c/a = 1

Product of the roots = 4 (given)

That is, c/a = 4

p²/1 = 1

p² = 1 -------------> p = ± 1

Example 10 :

Find the sum and product of roots of the quadratic equation given below.

Solution :

First let us write the given quadratic equation in general form.

Solution :

Now, the given equation is in general form. If we compare it to the general form, we get  a = 2, b = -9 and c = -6.

Sum of the roots = -b/a = -(-9)/2 = 9/2

Product of the roots = -6/2 = -3

After having gone through the stuff and example problems explained on "Sum and product of the roots of a quadratic equation examples",  we hope that the students would have understood how to do problems on "Sum and product of the roots of a quadratic equation examples"

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