What is the condition necessary for both of the roots of a quadratic to be real and negative?

CONDITIONS FOR BOTH ROOTS TO BE REAL & NEGATIVE: (1) If D > 0, there will be REAL roots. (2) If D>0, & all terms of the quadratic equation are positive then both roots will be NEGATIVE.

What is the condition for both roots to be positive?

So in summary, both roots are real positive numbers if and only if c>0 and b≤−2√c.

Under what conditions are the roots of a quadratic?

Step-by-step explanation: For the roots of the quadratic equation ax2+bx+c=0 to be real and distinct (unequal), the value of discriminant Δ=b2−4ac should be greater than 0. Given quadratic equation is x2+px+q=0. Comparing with the general quadratic equation, we get, a = 1, b = p and c = q.

What is the condition for real roots?

When a, b, c are real numbers, a 0: If = b² -4 a c = 0, then roots are equal (and real). If = b² -4 a c > 0, then roots are real and unequal. If = b² -4 a c < 0, then roots are complex.

What is the condition so that the roots of quadratic equation ax2 bx c 0 are real?

We also know that the roots of a quadratic equation are real if and only if the discriminant is non-negative, that is, if and only if b2−4c≥0. Using these facts, if α and β are both real and positive, then b=α+β>0, c=αβ>0 and b2≥4c, as above.

What is the appropriate required condition for a quadratic equation having real roots?

When a, b, and c are real numbers, a ≠ 0 and the discriminant is zero, then the roots α and β of the quadratic equation ax2+ bx + c = 0 are real and equal.

Can both roots of a quadratic equation be positive?

What is the condition for roots to be real?

Under what condition will the roots of the quadratic equation be real?

For the roots of the quadratic equation to be real and distinct (unequal), the value of discriminant should be greater than 0.

Under what conditions roots of a quadratic equation is real and unequal?

When a, b and c are real numbers, a ≠ 0 and discriminant is positive (i.e., b2 – 4ac > 0), then the roots α and β of the quadratic equation ax2 + bx + c = 0 are real and unequal.

What is the condition of quadratic equation?

When a, b, and c are real numbers, a ≠ 0 and the discriminant is zero, then the roots α and β of the quadratic equation ax2+ bx + c = 0 are real and equal. Case III: b2– 4ac < 0.

What is the condition for common root of quadratic equations?

Condition for Common Root of Quadratic Equations. In elementary algebra, the quadratic formula is the solution of the quadratic equation. There are other ways to solve the quadratic equation instead of using the quadratic formula, such as factoring, completing the square, or graphing. Using the quadratic formula is often the most convenient way.

How to find the real and imaginary roots of a quadratic equation?

The quadratic equation will have imaginary roots i.e α = (p + iq) and β = (p – iq). Where ‘iq’ is the imaginary part of a complex number: If the value of discriminant (D) > 0 i.e. b 2 – 4ac > 0: The quadratic equation will have real roots: If the value of discriminant > 0 and D is a perfect square: The quadratic equation will have rational roots

How to find the root of a quadratic equation with opposite sign?

The roots of quadratic equation are equal in magnitude but of opposite sign if b = 0 and ac < 0; The root with greater magnitude is negative if the sign of a = sign of b × sign of c; If a > 0, c < 0 or a > 0, c > 0; the roots of quadratic equation will have opposite sign; If y = ax 2 + bx + c is positive for all real values of x, a > 0 and D < 0

How many roots does the equation d = 0 have?

Since D>0, the equation will have two real and distinct roots. The roots are: Since D<0, the equation will have two distinct Complex roots. The roots are: Since D = 0, the equation will have two real and equal roots.