let a b c be three real numbers such that 2a 3b 6c 0 then

Let $$a, b, c$$ be three real numbers such that $$2a + 3b + 6c = 0.$$ Then the quadratic equation $$a{x^2} + bx + c = 0$$ has

A. imaginary roots

B. at least one root in $$(0, 1)$$

C. at least one root in $$(- 1, 0)$$

D. both roots in $$(1, 2)$$

Answer : at least one root in $$(0, 1)$$

Solution :
Take the equation $$2a{x^3} + 3b{x^2} + 6cx = 0.$$ Clearly, $$x = 0, 1$$ are two roots. Observe that $$a{x^2} + bx + c = 0$$ is the derived equation. So, one root lies between 0 and 1.

Releted MCQ Question on
Algebra >> Quadratic Equation

Releted Question 1

If $$\ell ,m,n$$ are real, $$\ell \ne m,$$ then the roots by the equation: $$\left( {\ell - m} \right){x^2} - 5\left( {\ell + m} \right)x - 2\left( {\ell - m} \right) = 0$$ are

A. Real and equal

B. Complex

C. Real and unequal

D. None of these

View Answer

Releted Question 2

The equation $$x + 2y + 2z = 1{\text{ and }}2x + 4y + 4z = 9{\text{ have}}$$

A. Only one solution

B. Only two solutions

C. Infinite number of solutions

D. None of these

View Answer

Releted Question 3

Let $$a > 0, b > 0$$ and $$c > 0$$ . Then the roots of the equation $$a{x^2} + bx + c = 0$$

A. are real and negative

B. have negative real parts

C. both (A) and (B)

D. none of these

View Answer

Releted Question 4

Both the roots of the equation $$\left( {x - b} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - b} \right) = 0$$ are always

A. positive

B. real

C. negative

D. none of these.

View Answer

Let $$a, b, c$$ be three real numbers such that $$2a + 3b + 6c = 0.$$ Then the quadratic equation $$a{x^2} + bx + c = 0$$ has

Releted MCQ Question on
Algebra >> Quadratic Equation

If $$\ell ,m,n$$ are real, $$\ell \ne m,$$ then the roots by the equation: $$\left( {\ell - m} \right){x^2} - 5\left( {\ell + m} \right)x - 2\left( {\ell - m} \right) = 0$$ are

The equation $$x + 2y + 2z = 1{\text{ and }}2x + 4y + 4z = 9{\text{ have}}$$

Let $$a > 0, b > 0$$ and $$c > 0$$ . Then the roots of the equation $$a{x^2} + bx + c = 0$$

Both the roots of the equation $$\left( {x - b} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - b} \right) = 0$$ are always

Practice More Releted MCQ Question on
Quadratic Equation

Practice More MCQ Question on Maths Section

Let $$a, b, c$$ be three real numbers such that $$2a + 3b + 6c = 0.$$ Then the quadratic equation $$a{x^2} + bx + c = 0$$ has

Releted MCQ Question on Algebra >> Quadratic Equation

If $$\ell ,m,n$$ are real, $$\ell \ne m,$$ then the roots by the equation: $$\left( {\ell - m} \right){x^2} - 5\left( {\ell + m} \right)x - 2\left( {\ell - m} \right) = 0$$ are

The equation $$x + 2y + 2z = 1{\text{ and }}2x + 4y + 4z = 9{\text{ have}}$$

Let $$a > 0, b > 0$$ and $$c > 0$$ . Then the roots of the equation $$a{x^2} + bx + c = 0$$

Both the roots of the equation $$\left( {x - b} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - b} \right) = 0$$ are always

Practice More Releted MCQ Question on Quadratic Equation

Practice More MCQ Question on Maths Section

Releted MCQ Question on
Algebra >> Quadratic Equation

Practice More Releted MCQ Question on
Quadratic Equation