Question

.
Find the nature of the roots of the following quadratic equations. If
roots are real, find them.
(a) 5x2 - 3x + 2 = 0.
(b) 2x2 - 9x + 9 = 0.​

Answer 1

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Step by step solution:

$Given \ p(x)=5x^2 - 3x + 2 = 0.\\\\q(x)=2x^2 - 9x + 9 = 0\\\\we \ have \ to \ find \ nature \ of \ the \ roots.\\\\For \ nature \ we \ know \ that \ there \ are \ three \ case\\ \\D=b^2-4ac\\\\when \ D=0 \ (Quadratic \ equation \ has \ two \ real \ and \ equals \ root)\\\\D\geq0 \ (Quadratic \ equation \ has \ two \ real \ but \ unequals \ roots)\\\\D\leq0 \ (Quadratic \ equation \ has \ imagery \ roots)\\\\p(x)=5x^2 - 3x + 2 = 0\\\\D=9-40=(-31)\\\\D\leq0\\\\So \ p(x) \ has \ imagery \ roots$

$q(x)= 2x^2 - 9x + 9 = 0\\\\D=81-72=(9)\\\\D\geq0\\\\So \ q(x) \ has \ two \ real \ but \ unequals \ roots$

Hope it is clear to you.