For the equation a x 2-b x-c-0 which of the following statements is incorrect-a If b2-4 a c0 and b2-4 a c is a perfect square- then the roots are rational and unequal-d b2-4 a c-0- the roots are irrational-

(d) (b2 nbsp; minus; 4ac) nbsp; lt; nbsp;0, the roots are irrational. If #160;(b2 #160; #8722; #160;ac) #160; #60; #160;0, #160;the ...

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Mathematics

Irrational Numbers

For the equat...

Question

For the equation $a x^{2} + b x + c = 0$ which of the following statements is incorrect?
(a) If (b² − 4ac) < 0, the roots are imaginary.
(b) If (b² − 4ac) = 0, the roots are real and equal.
(c) If (b² − 4ac) > 0 and (b² − 4ac) is a perfect square, then the roots are rational and unequal.
(d) (b² − 4ac) < 0, the roots are irrational.

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Solution

(d) (b²− 4ac) < 0, the roots are irrational.

$If (b^{2} - a c) < 0, the roots may be rational or irrational .$

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(d) (b2 − 4ac) < 0, the roots are irrational. If (b2 − ac) < 0, the roots may be rational or irrational.

(d) (b²− 4ac) < 0, the roots are irrational.

$If (b^{2} - a c) < 0, the roots may be rational or irrational .$