1sec ≫ First term ≫ Algebra ≫ Unit 1 ≫ 1 - 3 Determining the Types of the two Roots of a Quadratic Equation.
(Q1 To Q10)
(1) The two roots of the equation: $x^2 - 5x + 11 = 0$ are:
(a) two complex and non-real roots.
(b) two rational roots.
(c) two different real roots.
(d) two equal real roots.
The correct answer is (a) two complex and non-real roots.
(2) The two roots of the equation: $x(x-2)=5$ are:
(a) two complex and non-real roots.
(b) two equal real roots.
(d) two different real roots.
(c) 2 and zero.
The correct answer is (c) two different real roots.
(3) If the roots of the equation: $\mathrm{k} x^2 - 8 x + 16 = 0$ are two complex and non-real, then:
(a) $\mathrm{k} > 2$
(b) $\mathrm{k} < 2$
(c) $\mathrm{k} \in ]1, 10[$
(d) $\mathrm{k} > 1$
The correct answer is (d) $\mathrm{k} > 1$.
(4) Determine the type of the two roots of the following equation:
$x^2 - 2x + 5 = 0$
The correct answer is: two complex and non-real roots.
(5) Determine the type of the two roots of the following equation:
$x^2 - 10x + 25 = 0$
The correct answer is: two equal real roots.
(6) Determine the type of the two roots of the following equation:
$-x^2 + 5x - 30 = 0$
The correct answer is: The two roots are complex and not real numbers.
(7) Determine the type of the two roots of the following equation:
$(x - 11) - x(x - 6) = 0$
The correct answer is: The two roots are real and different..
(8) Determine the type of the two roots of each of the following equations:
$(x - 1)(x - 7) = 2(x - 3)(x - 4)$
The correct answer is: The two roots are complex and not real.
(9) If the two roots of each of the following quadratic equations are equal, find the value of $k$:
$x^2 - 3x + 2 + \frac{1}{k} = 0$
The correct answer is: $4$.
(10) If the two roots of each of the following quadratic equation are equal, find the value of $k$:
$x^2 + 2(k - 1)x + (2k + 1) = 0$, then find the two roots.
The correct answer is: $0,1,1$ or $4,-3,-3$.
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