It is known that the image of quadratic function y = ax ^ 2 + BX + C (a > 0) has two different intersections with x-axis, if f (c) = 0 and 0

It is known that the image of quadratic function y = ax ^ 2 + BX + C (a > 0) has two different intersections with x-axis, if f (c) = 0 and 0

(1) The condition that C is not 0 is required
Because a * C ^ 2 + b * C + C = 0,
Then a * C + B + 1 = 0
In this case, f (1 / a) = 1 / A + B / A + C = (B + 1) / A + C = 0
（2）
Substituting B = - ac-1 into Zhi:
F (x) = ax ^ 2-acx-x + C = (x-C) (AX-1), so 0

If TaNx / tanx-1 = - 1, find sin (π / 2 + x) cos (3 π / 2-x)

The left is equivalent to TaNx = 1-tanx
Equivalent to TaNx = 0.5
So SiNx = root of five
Cosx = two fifths root sign five
What you seek is equivalent to cosx times SiNx
Equal to 0.4

It is known that sin (pai-x) + cos (PAI + x) = 1 / 5 (0

∵sin(π-x)+cos(π+x)=1/5==>sinx-cosx=1/5.(1)==>(sinx-cosx)²=1/25==>2sinxcosx=24/25∴(sinx+cosx)²=sin²x+2sinxcosx+cos²x=1+2sinxcosx=1+24/25=49/25∴sinx+cosx=±7/5.(2)∵0

It is known that TaNx = - √ 2, π

tanx=-√2,π