A root is a part of the plant that grows underground and absorbs water and nutrients from soil. It anchors the plant firmly and stores food. Roots can be thin or thick fibrous or taproots spreading deep in soil and helping plants survive in harsh weather conditions.
Quadratic equations are mathematical expressions in the form ax² + bx + c = 0 where a b and c are real numbers and a ≠ 0. The chapter covers methods to find solutions including factorization square completion and quadratic formula. Students learn to identify roots analyze discriminant determine nature of roots and solve real-life problems. Understanding this topic helps in higher mathematics particularly in algebra calculus and geometry applications. The chapter builds foundation for complex numbers and higher degree equations.
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Given equation: x² – 4x + 5 = 0
For nature of roots check discriminant:
b² – 4ac
Here:
a = 1
b = -4
c = 5
Discriminant = (-4)² – 4(1)(5)
= 16 – 20
= -4
Since discriminant < 0:
The roots are imaginary (or complex conjugates)
We can verify:
Using quadratic formula:
x = [4 ± √(-4)]/2
x = 2 ± i
Therefore roots are complex conjugates: 2 + i and 2 – i
Hence, the nature of roots is Imaginary.
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