Q: For what value of $k$ does the quadratic equation $x^2 - kx + 9 = 0$ have equal real roots?

The given quadratic equation is $x^2 - kx + 9 = 0$. \nComparing with $ax^2 + bx + c = 0$, we have: $a = 1, b = -k, c = 9$ \nFor equal real roots, the discriminant must be zero ($D = 0$): $D = b^2 - 4ac = 0$ $(-k)^2 - 4(1)(9) = 0$ $k^2 - 36 = 0$ $k^2 = 36$ $k = \pm 6$ \nTherefore, the correct option

Q: What is the nature of the roots of the quadratic equation $2x^2 - 4x + 3 = 0$?

For the given quadratic equation $2x^2 - 4x + 3 = 0$: \nComparing with the standard form $ax^2 + bx + c = 0$: $a = 2$ $b = -4$ $c = 3$ \nThe discriminant ($D$) is given by: $$D = b^2 - 4ac$$ $$D = (-4)^2 - 4(2)(3)$$ $$D = 16 - 24 = -8$$ \nSince $D

Question 1

For what value of $k$ does the quadratic equation $x^2 - kx + 9 = 0$ have equal real roots?

Accepted Answer

The given quadratic equation is $x^2 - kx + 9 = 0$. 
Comparing with $ax^2 + bx + c = 0$, we have: $a = 1, b = -k, c = 9$ 
For equal real roots, the discriminant must be zero ($D = 0$): $D = b^2 - 4ac = 0$ $(-k)^2 - 4(1)(9) = 0$ $k^2 - 36 = 0$ $k^2 = 36$ $k = \pm 6$ 
Therefore, the correct option

Question 2

What is the nature of the roots of the quadratic equation $2x^2 - 4x + 3 = 0$?

Accepted Answer

For the given quadratic equation $2x^2 - 4x + 3 = 0$: 
Comparing with the standard form $ax^2 + bx + c = 0$: $a = 2$ $b = -4$ $c = 3$ 
The discriminant ($D$) is given by: $$D = b^2 - 4ac$$ $$D = (-4)^2 - 4(2)(3)$$ $$D = 16 - 24 = -8$$ 
Since $D

Question 3

What is the standard form of a quadratic equation?

Accepted Answer

The standard form of a quadratic equation in the variable x is represented mathematically as ax² + bx + c = 0, where a, b, and c are real numbers, and the coefficient of x squared, denoted by 'a', must not be equal to zero. If 'a' becomes zero, the equation reduces to a linear equation and is no lon

Question 4

Define the discriminant of a quadratic equation and write its formula.

Accepted Answer

The discriminant of a quadratic equation is a very important mathematical value that determines the nature of the roots of that equation without actually solving it fully. For a standard quadratic equation given by ax² + bx + c = 0, the discriminant is denoted by the capital letter 'D' or by the del

Question 5

Write the quadratic formula (Sridharacharya formula) for solving a quadratic equation.

Accepted Answer

The quadratic formula, also famously known as the Sridharacharya formula in Indian mathematics, is used to find the roots of any given quadratic equation in the standard form ax² + bx + c = 0. The complete mathematical expression for this formula is x = (-b ± √(b² - 4ac)) / (2a), provided that the l

Quadratic Equations