What are the roots of the equation 2x 2 7x 3 0?

What are the roots of the equation 2x 2 7x 3 0?

Answer. Hence, the roots of the given equation are 3 & ½.

What is completing Square?

Completing the Square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial . To solve ax2+bx+c=0 by completing the square: Add the square of half the coefficient of the x -term, (b2a)2 to both sides of the equation.

For what value of M will the quadratic equation x2 MX 4 0 have real and equal roots?

In the given equation x2 – mx + 4 = 0, a = 1, b = -m and c = 4. Therefore, the discriminant b2 – 4ac = m2 – 4(4)(1) = m2 – 16. The roots of the given equation are real and equal. Therefore, m2 – 16 = 0 or m2 = 16 or m = +4 or m = -4.

Which of the following is an example for quadratic equation?

Here are examples of other forms of quadratic equations: x(x – 2) = 4 [upon multiplying and moving the 4 becomes x² – 2x – 4 = 0] x(2x + 3) = 12 [upon multiplying and moving the 12 becomes 2x² – 3x – 12 = 0] 3x(x + 8) = -2 [upon multiplying and moving the -2 becomes 3x² + 24x + 2 = 0]

What are roots in quadratic equations?

Roots are also called x-intercepts or zeros. A quadratic function is graphically represented by a parabola with vertex located at the origin, below the x-axis, or above the x-axis. Therefore, a quadratic function may have one, two, or zero roots. The roots of a function are the x-intercepts.

What is nature of roots in math?

The discriminant determines the nature of the roots of a quadratic equation. The word ‘nature’ refers to the types of numbers the roots can be — namely real, rational, irrational or imaginary. If Δ≥0, the expression under the square root is non-negative and therefore roots are real.

Can a quadratic equation have more than 2 roots?

Theorem : A quadratic equation cannot have more than two roots. Proof : Let us consider α,β and γ are the three roots of the given quadratic equation ax2 a x 2 + bx + c = 0, where a,b,c ϵ R and a \ne 0. Then each α,β and γ will satisfy this quadratic equation.

Can a quadratic equation have 3 roots?

Therefore, our assumption that a quadratic equation has three distinct real roots is wrong. Hence, every quadratic equation cannot have more than 2 roots. Note: If a condition in the form of a quadratic equation is satisfied by more than two values of the unknown then the condition represents an identity.