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प्रश्न
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 4x + 1 = 0
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उत्तर
x2 - 4x + 1 = 0
Here, a = 1, b = -4 and c = 1
D = b2 - 4ac
⇒ 16 - 4 x 1 x 1
⇒ 16 - 4
= 12 > 0
The given equation has real roots.
संबंधित प्रश्न
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 (s) of k for which each of the following quadratic equation has equal roots : kx2 – 4x – 5 = 0
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
Discuss the nature of the roots of the following equation: `5x^2 - 6sqrt(5)x + 9` = 0
If roots of a quadratic equation 3y2 + ky + 12 = 0 are real and equal, then find the value of ‘k’.
Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots are:
The value of k for which the equation x2 + 2(k + 1)x + k2 = 0 has equal roots is:
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Complete the following activity to determine the nature of the roots of the quadratic equation x2 + 2x – 9 = 0 :
Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
a = 1, b = 2, c = `square`
∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
∴ b2 – 4ac > 0
∴ The roots of the equation are real and unequal.
