"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,

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 = 3****x² + 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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