Let a, b ∈ R be such that the equation ax2 – 2bx + 15 = 0 has a repeated root α. If α and β are the roots of the equation x2 – 2bx + 21 = 0, then α2 + β2 is equal to
- 37
- 58
- 68
- 92
The Correct Option is A
Solution and Explanation
The correct option is(B): 58.
ax2 – 2bx + 15 = 0 has repeated root so b2 = 15a
and
\(α=\frac{15}{b}\)
∵α is a root of x2 – 2bx + 21 = 0
So
\(\frac{225}{b^2}=9⇒b^2=25\)
Now α2 + β2 = (α + β)2 – 2αβ = 4b2 – 42 = 100 – 42
= 58
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Concepts Used:
Root
A Root refers to the vascular part of any plant which is pinpointed or discovered at the lowest level and is entirely responsible for connecting the plant with the soil. It absorbs water (H20), minerals, nutrients, etc., and further feeds the plant for its development. Roots are also responsible for acting as the repository for food and nutrients of the plant.
Read More: Plant Roots
Characteristics of Roots:
- Roots are homogeneous in nature due to their potential to work towards producing similar organs like secondary or tertiary roots from the pericycle.
- Roots can be examined as positively Geotropic and Hydrotropic but negatively Phototropic.
Functions of Roots:
- The roots are in charge of providing a systematic connection to the different parts of the plant.
- It is also accountable for the storage of the reserved food material and the synthesis for the growth of the plant.