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complex number and quadratic equation | class 11 math book

**class 11 math in hindi. complex numbers and quadratic equations class 11 pdf**
**How are complex numbers related to quadratic equations?**
**In relation to quadratic equations, imaginary numbers (and complex numbers) occur when the value under the radical portion of the quadratic formula is negative. When this occurs, the equation has no roots (zeros) in the set of real numbers. ... These complex roots will be expressed in the form a + bi.**

**What is a complex solution?**
**In Algebra 1, you found that certain quadratic equations had negative square roots in their solutions. ... The roots belong to the set of complex numbers, and will be called "complex roots" (or "imaginary roots"). These complex roots will be expressed in the form a ± bi.**

**Does the quadratic formula work for complex coefficients?**
**The quadratic equations with complex coefficients that means the coefficientsof the equations are not real numbers, they may be an imaginary numbers(i).Quadratic equation as, a x 2 + b x + c = 0 where a,b,c are complex numbers and a 0. (i) if D = - 4ac = 0 then the roots are complex and equal.**

**What are real and complex roots?**
**Complex Roots. In general, a root is the value which makes polynomial or function as zero. ... In the quadratic equation ax**^{2}+bx+c=0, a, b, c are real numbers, the discriminant b^{2} –4ac< 0, then its roots are complex roots. Moreover, the complexnumber's form is a+ib, where a and b are real numbers.

Why can't a quadratic equation have an imaginary solution?
The statement should should read a **quadratic equation** with real coefficients **can't have** only one **imaginary** root. The reason being in x 2 + a x + c = 0 because is sum of the roots and is product of the roots. But are both real numbers, that is impossible if only one of the roots were **imaginary.**
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