SUM AND PRODUCT OF ROOTS OF QUADRATIC EQUATION PDF

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"Sum and product of roots of quadratic equation pdf" is nothing but the pdf document which contains practice questions on the above mentioned stuff.

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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,

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,

Problems

Let us see the step by step solution for the problems found on "Sum and product of roots of quadratic equation pdf"

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 roots of quadratic equation pdf"

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 step by step solutions for all the problems found in "Sum and product of roots of quadratic equation pdf",  we hope that the students would have understood how to do problems on "Sum and product of roots of a quadratic equation pdf"

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