If A and B are of opposite sign ,then solution of ax + b = 0 is always be of which sign.
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We know that the discriminant D of a quadratic equation ax
2
+bx+c=0 is:
D=b
2
−4ac
Since it is given that a and c are of opposite signs, therefore, we consider the following cases:
Case 1: If a>0 and c<0 then
ac<0
⇒−ac>0
Therefore, we have:
D=b
2
−4ac=b
2
+4(−ac)=b
2
+4(−ac)>0(∵−ac>0)
⇒D>0
Case 2: If a<0 and c>0 then
ac<0
⇒−ac>0
Therefore, as done in case 1:
D=b
2
−4ac>0
Hence, the roots of the quadratic equation ax
2
+bx+c=0 are real and distinct.
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