Advertisements
Advertisements
Question
Complete the following activity to find the value of discriminant for quadratic equation 4x2 – 5x + 3 = 0.
Activity: 4x2 – 5x + 3 = 0
a = 4, b = ______, c = 3
b2 – 4ac = (–5)2 – (______) × 4 × 3
= ( ______ ) – 48
b2 – 4ac = ______
Advertisements
Solution
4x2 – 5x + 3 = 0
a = 4, b = –5, c = 3
b2 – 4ac = (–5)2 – 4 × 4 × 3
= 25 – 48
∴ b2 – 4ac = −23
APPEARS IN
RELATED QUESTIONS
Solve the equation by using the formula method. 3y2 +7y + 4 = 0
Solve the following quadratic equation for x :
9x2 − 6b2x − (a4 − b4) = 0
Find the values of k for which the quadratic equation (3k + 1) x2 + 2(k + 1) x + 1 = 0 has equal roots. Also, find the roots.
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 – 3x + 5 = 0
Find the value of k for which the roots are real and equal in the following equation:
3x2 − 5x + 2k = 0
Find the values of k for which the roots are real and equal in the following equation:
x2 – 4kx + k = 0
If 1 is a root of the quadratic equation 3x2 + ax – 2 = 0 and the quadratic equation a(x2 + 6x) – b = 0 has equal roots, find the value of b ?
Write the value of k for which the quadratic equation x2 – kx + 4 = 0 has equal roots.
Determine the nature of the roots of the following quadratic equation :
2x2 + 5x - 6 = 0
Solve the following quadratic equation using formula method only :
`2x + 5 sqrt 3x +6= 0 `
Solve the following quadratic equation using formula method only
3a2x2 +8abx + 4b2 = 0, a ≠ 0
In each of the following determine the; value of k for which the given value is a solution of the equation:
3x2 + 2kx - 3 = 0; x = `-(1)/(2)`
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 5x + 7 = 0
Discuss the nature of the roots of the following quadratic equations : `2sqrt(3)x^2 - 5x + sqrt(3)` = 0
Choose the correct answer from the given four options :
The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)
Which of the following equations has no real roots?
If the equation x2 – (2 + m)x + (–m2 – 4m – 4) = 0 has coincident roots, then:
Which of the following equations has the sum of its roots as 3?
Solve for x: `5/2 x^2 + 2/5 = 1 - 2x`.
The probability of selecting integers a ∈ [–5, 30] such that x2 + 2(a + 4)x – 5a + 64 > 0, for all x ∈ R, is ______.
