Podcast
Questions and Answers
For what values of $p$ does the quadratic equation $x^2 - px + 1 = 0$ have no real roots?
For what values of $p$ does the quadratic equation $x^2 - px + 1 = 0$ have no real roots?
- $p > 2$
- $-2 < p < 2$ (correct)
- $p < -2$
- $-3 < p < 3$
Given the quadratic polynomial $3x^2 + 10x + 8$, what are its zeroes?
Given the quadratic polynomial $3x^2 + 10x + 8$, what are its zeroes?
- $2$ and $\frac{4}{3}$
- $-2$ and $\frac{-4}{3}$ (correct)
- $-2$ and $\frac{4}{3}$
- $2$ and $\frac{-4}{3}$
If the quadratic equation $ax^2 + bx + c = 0$ has real and distinct roots, which of the following statements is true regarding its discriminant?
If the quadratic equation $ax^2 + bx + c = 0$ has real and distinct roots, which of the following statements is true regarding its discriminant?
- $b^2 - 4ac \le 0$
- $b^2 - 4ac < 0$
- $b^2 - 4ac > 0$ (correct)
- $b^2 - 4ac = 0$
A quadratic equation is given by $x^2 + kx + 4 = 0$. If the equation has exactly one real root, what is the value of $k$?
A quadratic equation is given by $x^2 + kx + 4 = 0$. If the equation has exactly one real root, what is the value of $k$?
The sum and product of the zeroes of a quadratic polynomial are 5 and 6, respectively. Which of the following represents the quadratic polynomial?
The sum and product of the zeroes of a quadratic polynomial are 5 and 6, respectively. Which of the following represents the quadratic polynomial?
For a quadratic equation $ax^2 + bx + c = 0$, if $a$ and $c$ have opposite signs, which of the following must be true?
For a quadratic equation $ax^2 + bx + c = 0$, if $a$ and $c$ have opposite signs, which of the following must be true?
Given the quadratic polynomial $f(x) = ax^2 + bx + c$, if the graph of $f(x)$ opens downward, which of the following is true?
Given the quadratic polynomial $f(x) = ax^2 + bx + c$, if the graph of $f(x)$ opens downward, which of the following is true?
If $\alpha$ and $\beta$ are the roots of the quadratic equation $2x^2 - 5x + 3 = 0$, what is the value of $\frac{1}{\alpha} + \frac{1}{\beta}$?
If $\alpha$ and $\beta$ are the roots of the quadratic equation $2x^2 - 5x + 3 = 0$, what is the value of $\frac{1}{\alpha} + \frac{1}{\beta}$?
A line passes through the point (3,1) and has a slope of 2. Find the y-intercept of this line?
A line passes through the point (3,1) and has a slope of 2. Find the y-intercept of this line?
Given the points (1, 2) and (3, 6), determine the equation of the line that passes through these points.
Given the points (1, 2) and (3, 6), determine the equation of the line that passes through these points.
Flashcards
Condition for no real roots of x² – px + 1 = 0?
Condition for no real roots of x² – px + 1 = 0?
A quadratic equation has no real roots if its discriminant (b^2 - 4ac) is less than zero. In x^2 - px + 1 = 0, a=1, b=-p, and c=1. The condition for no real roots is p^2 - 4 < 0.
If x² - px + 1 = 0 has no real roots, what is range of 'p'?
If x² - px + 1 = 0 has no real roots, what is range of 'p'?
If x² - px + 1 = 0 has no real roots, then -2 < p < 2.
The zeroes of 3x² + 10x + 8?
The zeroes of 3x² + 10x + 8?
To find the zeroes, solve 3x² + 10x + 8 = 0. Factor: (3x + 4)(x + 2) = 0. Thus, the zeroes are x = -4/3 and x = -2.
Study Notes
- Section A consists of 20 questions worth 1 mark each.
Equation Roots
- For the equation x² – px + 1 = 0 to not possess real roots, the following condition must be met: -2 < p < 2
Quadratic Polynomial Zeroes
- The zeroes of the quadratic polynomial 3x² + 10x + 8 are: -2 and -(4/3)
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