Q. 1 A3.7( 19 Votes )

# Find whether the following equations have real roots. If real roots exist, find them.

8x^{2} + 2x – 3 = 0

Answer :

To check whether the quadratic equation has real roots or not, we need to check the discriminant value i.e.,

D = b^{2} - 4ac

Given, 8x^{2} + 2x – 3 = 0

**∴** D = 2^{2} - 4(8) (-3)

⇒D = 4 + 96 > 0

Hence, the roots are real and distinct.

To find the roots, use the formula,

Rate this question :

The sum of two numbers is 18 and the sum of their reciprocals is . Find the numbers.

KC Sinha - MathematicsDivide 12 into two parts such that their product is 32.

KC Sinha - MathematicsThe sum of the squares of three consecutive positive integers is 50. Find the integers.

KC Sinha - MathematicsThe difference of two numbers is 4. If the difference of their reciprocals is , find the two numbers.

KC Sinha - MathematicsThe difference of squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.

KC Sinha - MathematicsThe sum of a number and its reciprocal is . Find the number.

KC Sinha - MathematicsThe difference of two numbers is 5 and the difference of their reciprocals is Find the numbers.

KC Sinha - MathematicsDivide 12 into two parts such that the sum of their squares is 74.

KC Sinha - MathematicsTwo numbers differ by 3 and their product is 504. Find the numbers.

KC Sinha - Mathematics