# Find constant coefficients in cubic equation given intercepts and gradient at point

Taken from an exercise:

The graph of $y = ax^3 + bx^2 + cx + d$ touches the x-axis at $x = -2$. The graph also cuts the y-axis at $y = 5$ with a gradient of 3. Find $a$, $b$, $c$ and $d$.

I've been able to find $c$ and $d$ but not $a$ or $b$.

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Hint: It sounds like you got $c$ and $d$ from the fact that it goes through $(0,5)$ with slope $3$. Now we know it is $y=ax^3+bx^2+3x+5$. To get $a$ and $b$ you need to use the information at $(-2,0)$. "Touches" sounds like a double root. You should be able to substitute the $c$ and $d$ you have with the fact that it passes through $(-2,0)$ with zero slope to find $a$ and $b$.