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प्रश्न
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x – 1)(x + 2) + 2 = 0
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उत्तर
The equation (x – 1)(x + 2) + 2 = 0 has two real and distinct roots.
Simplifying the above equation,
x2 – x + 2x – 2 + 2 = 0
x2 + x = 0
D = b2 – 4ac
= 12 – 4(1)(0)
= 1 – 0 > 0
Hence, the roots are real and distinct.
APPEARS IN
संबंधित प्रश्न
Solve for x: `1/(x+1)+2/(x+2)=4/(x+4), `x ≠ -1, -2, -3
Without solving, examine the nature of roots of the equation 4x2 – 4x + 1 = 0
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 – 3x + 5 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 + kx + 9 = 0
Find the values of k for which the roots are real and equal in the following equation:
2x2 + kx + 3 = 0
Find the value of the discriminant in the following quadratic equation:
2x2 - 3x + 1 = O
Solve the following quadratic equation using formula method only
x2 - 4x - 1 = 0
Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.
Solve x2/3 + x1/3 - 2 = 0.
Determine whether the given quadratic equations have equal roots and if so, find the roots:
3x2 - 6x + 5 = 0
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State whether the following quadratic equation have two distinct real roots. Justify your answer.
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Find the value of 𝑚 so that the quadratic equation 𝑚𝑥(5𝑥 − 6) = 0 has two equal roots.
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.
Solve the following quadratic equation:
x2 + 4x – 8 = 0
Give your Solution correct to one decimal place.
(Use mathematical tables if necessary.)
