Question

Find the roots of 5x²-7x+6=0 by using quadratic formula




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Answer 1

Topic :-

Complex number and quadratic equations

Given :-

Quadratic equation is 5x² - 7x + 6 = 0

To find :-

Roots of the given equation by using quadratic formula.

Solution :-

If the roots of a quadratic equation are imaginary, i.e. not real, they exists in the form of conjugate i.e. one of the root will be of the form x + iy and another will be of the form x - iy.

Inorder to solve this problem, we must have a basic knowledge about complex numbers.

A complex number is an imaginary number which is of the form a + bi where a is the real part of complex number and b is the imaginary part of complex number.

For ex - We cannot solve square root for negative numbers, but we can represent them in terms of iota which is denoted with i. Value of i is √-1 and by using this, we can also express negative squared numbers such as √-3 = 3i and √-9 = 3i and so on.

Now let's proceed by using quadratic formula to find the roots of given equation!

General form of quadratic equation is :-

• ax² + bx + c = 0

By comparing the given equation with general form of quadratic equation, we get :-

• a = 5
• b = - 7
• c = 6

Quadratic Formula

$\underline{\boxed{\sf Roots = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}}$

By substituting the given values in this formula, we get :

$\sf Roots = \dfrac{-( - 7)\pm\sqrt{( - 7)^2-4(5)(6)}}{2(5)}$

$\sf Roots = \dfrac{7\pm\sqrt{49-120}}{10}$

$\sf Roots = \dfrac{7\pm\sqrt{ - 71}}{10}$

$\sf Roots = \dfrac{7\pm\sqrt{ 71}i}{10}$

Hence these are the required roots or zeroes of the given equation.