plsss... help to solve this above question
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(a) cannot both be negative.
Reason : Let p(x) = x2 + kx + k, k≠0
On comparing p(x) with ax2 + bx + c, we get
a=1, b=k, c= k
x=(-b±√b²-4ac)/2
= [-k±√(k²-4k)]/2
= [-k±√k(k-4)]/2 ,k≠0
Here, k(k-4)=0
In quadratic polynomial ax2 + bx + c
If a > 0, b> 0, c> 0 or a< 0, b< 0,c< 0,
then the polynomial has always all negative zeroes.
and if a > 0, c < 0 or a < 0, c > 0, then the polynomial has always zeroes of opposite sign
Case I :-
⇒ a = 1>0, b,c = k<0
So, both zeroes are of opposite sign.
Case II :-
⇒ a = 1> 0, b,c>4
So, both zeroes are negative.
Hence, in any case zeroes of the given quadratic polynomial cannot both be positive.
Reason : Let p(x) = x2 + kx + k, k≠0
On comparing p(x) with ax2 + bx + c, we get
a=1, b=k, c= k
x=(-b±√b²-4ac)/2
= [-k±√(k²-4k)]/2
= [-k±√k(k-4)]/2 ,k≠0
Here, k(k-4)=0
In quadratic polynomial ax2 + bx + c
If a > 0, b> 0, c> 0 or a< 0, b< 0,c< 0,
then the polynomial has always all negative zeroes.
and if a > 0, c < 0 or a < 0, c > 0, then the polynomial has always zeroes of opposite sign
Case I :-
⇒ a = 1>0, b,c = k<0
So, both zeroes are of opposite sign.
Case II :-
⇒ a = 1> 0, b,c>4
So, both zeroes are negative.
Hence, in any case zeroes of the given quadratic polynomial cannot both be positive.
rohitsethu3:
plsss give a detailed answer.....whyy
ok
If k>0 then the signs of f(−x)have the pattern +−+. With two changes of sign, the polynomial could have 2 or 0 negative zeros.
For example, with k=8 we have:
f(x)=x2+8x+8
f(x)=x2+8x+16−8
f(x)=(x+4)2−(2√2)2
f(x)=(x+4−2√2)(x+4+2√2)
which has zeros x=−4±2√2
So it is possible for both roots to be negative and (b) is definitely false. These roots are also unequal, so (d) is false.
For example, with k=8 we have:
f(x)=x2+8x+8
f(x)=x2+8x+16−8
f(x)=(x+4)2−(2√2)2
f(x)=(x+4−2√2)(x+4+2√2)
which has zeros x=−4±2√2
So it is possible for both roots to be negative and (b) is definitely false. These roots are also unequal, so (d) is false.
you'll dont get it :/ wait
yess bro ....will wait
mko bro bole:/
I have just edited my ans.
thank you so much bro!!!!
I'm not bro :(
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cannot both be negative
thank you so much bro!!!
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