If $x$ is real, then the minimum value of $x^2 - 8x+17 $ is
- 1
- 2
- 3
- 4
The Correct Option is A
Solution and Explanation
$=(x-4)^{2}-16+17$
$=(x-4)^{2}+1 $
$\Rightarrow y \,\geq 1$ for all real values of x as
$(x-4)^{2} \geq \,0$
Hence , minimum value of y is 1
Top Questions on Complex Numbers and Quadratic Equations
- Let $z=(1+i)(1+2i)(1+3i)\cdots(1+ni)$, where $i=\sqrt{-1}$. If $|z|^2=44200$, then $n$ is equal to
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Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
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- The number of distinct real solutions of the equation \[ x|x + 4| + 3|x + 2| + 10 = 0 \] is
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Questions Asked in KCET exam
Match the following:
In the following, \( [x] \) denotes the greatest integer less than or equal to \( x \).
Choose the correct answer from the options given below:- KCET - 2025
- Differentiability
- If \[ y = \frac{\cos x}{1 + \sin x} \] then:
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- Differentiability
- A function \( f(x) \) is given by:
\[ f(x) = \begin{cases} \frac{1}{e^x - 1}, & \text{if } x \neq 0 \\ \frac{1}{e^x + 1}, & \text{if } x = 0 \end{cases} \] Then, which of the following is true?- KCET - 2025
- Limits
- The function f(x) is given by:
For x < 0:
f(x) = ex + axFor x ≥ 0:
f(x) = b(x - 1)2
The function is differentiable at x = 0. Then,- KCET - 2025
- Differentiability
- The function \( f(x) = \tan x - x \)
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- Derivatives
Concepts Used:
Complex Numbers and Quadratic Equations
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b and c are the real numbers.
