Advertisements
Advertisements
प्रश्न
Determine the nature of root of the quadratic equation.
\[\sqrt{3} x^2 + \sqrt{2}x - 2\sqrt{3} = 0\]
उत्तर
\[\sqrt{3} x^2 + \sqrt{2}x - 2\sqrt{3} = 0\]
In order to find the nature of the roots we need to find the discriminant.
D = b2 - 4ac
\[a = \sqrt{3}, b = \sqrt{2}, c = - 2\sqrt{3}\]
\[D = \left( \sqrt{2} \right)^2 - 4 \times \sqrt{3} \times \left( - 2\sqrt{3} \right)\]
= 2 + 8 (3)
= 2 + 24
= 26 > 0
Since, the D > 0 so, real and unequal root.
APPEARS IN
संबंधित प्रश्न
Compare the given quadratic equation to the general form and write values of a, b, c.
x2 – 7x + 5 = 0
Compare the given quadratic equation to the general form and write values of a,b, c.
2m2 = 5m – 5
Solve using formula.
x2 – 3x – 2 = 0
Solve using formula.
3m2 + 2m – 7 = 0
Solve using formula.
5m2 – 4m – 2 = 0
Solve using formula.
y2 + `1/3`y = 2.
Solve using formula.
5x2 + 13x + 8 = 0
The roots of the following quadratic equation is real and equal, find k.
3y2 + ky +12 = 0
The roots of the following quadratic equation is real and equal, find k.
kx (x – 2) + 6 = 0
Find the value of discriminant of the following equation.
\[\sqrt{5} x^2 - x - \sqrt{5} = 0\]
Two roots of quadratic equation is given ; frame the equation.
10 and –10
Two roots of quadratic equation is given ; frame the equation.
\[1 - 3\sqrt{5} \text{ and } 1 + 3\sqrt{5}\]
Two roots of quadratic equation is given ; frame the equation.
0 and 7
Determine the nature of root of the quadratic equation.
m2 - 2m + 1 = 0
The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35, find the equation.
If α and β are the roots of the equation is 3x2 + x – 10 = 0, then the value of `1/α + 1/β` is ______.
If 2 and 5 are the roots of the quadratic equation, then complete the following activity to form quadratic equation:
Activity:
Let α = 2 and β = 5 are the roots of the quadratic equation.
Then quadratic equation is:
x2 − (α + β)x + αβ = 0
∴ `x^2 - (2 + square)x + square xx 5 = 0`
∴ `x^2 - square x + square = 0`
